Organizing Committee
Abstract

This Semester Program will bring together both leading experts and junior researchers to discuss the current state-of-the-art and emerging trends in computational PDEs. While there are scores of numerical methodologies designed for a wide variety of PDEs, the program will be designed around three workshops each centered around a specific theme: PDEs and Geometry, Nonlocal PDEs, and Numerical Analysis of Multiphysics problems. This grouping of topics embodies a broad representation of computational mathematics with each set possessing its own skill set of mathematical tools and viewpoints. Nonetheless, all workshops will have the common theme of using rigorous mathematical theory to develop and analyze the convergence and efficiency of numerical methods. The diversity of the workshop topics will bring together historically distinct groups of mathematicians to interact and facilitate new ideas and breakthroughs.

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Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee
  • Pedro Aceves Sanchez
    University of Arizona
    Apr 14-20, 2024
  • James Adler
    Tufts University
    Jan 29-May 4, 2024
  • Måns Andersson
    KTH Royal Institute of Technology
    Mar 11-15, 2024
  • Anca Andrei
    Tufts University
    Feb 12-16, 2024; Mar 11-15, 2024
  • Daniel Appelö
    Virginia Tech
    Jan 29-Mar 31, 2024
  • Douglas Arnold
    University of Minnesota
    Mar 3-30, 2024
  • Gerard Awanou
    University of Illinois, Chicago
    Mar 11-15, 2024
  • blanca ayuso de dios
    universita milano-bicocca
    Mar 31-May 4, 2024
  • Francis Aznaran
    University of Notre Dame
    Feb 12-16, 2024
  • Gabriel Barrenechea
    University of Strathclyde
    Feb 10-Mar 10, 2024
  • Soeren Bartels
    University of Freiburg
    Mar 7-27, 2024
  • Alex Bespalov
    University of Birmingham
    Apr 1-21, 2024
  • Florin Bobaru
    UNIVERSITY OF NEBRASKA–LINCOLN
    Apr 15-19, 2024
  • Andrea Bonito
    Texas A&M University
    Apr 15-19, 2024
  • Juan Pablo Borthagaray
    Universidad de la República, Uruguay
    Apr 15-19, 2024
  • Lucas Bouck
    Carnegie Mellon University
    Mar 11-15, 2024
  • Susanne Brenner
    Louisiana State University
    Feb 1-Apr 30, 2024
  • Sylvie Bronsard
    New York University
    Feb 12-16, 2024
  • Jed Brown
    University of Colorado Boulder
    Feb 12-16, 2024
  • Martina Bukač
    University of Notre Dame
    Feb 12-16, 2024
  • Olena Burkovska
    Oak Ridge National Laboratory
    Apr 15-19, 2024
  • Erik Burman
    University College London
    Mar 10-16, 2024
  • Suncica Canic
    University of California, Berkeley
    Feb 12-16, 2024
  • John Carter
    Rensselaer Polytechnic Institute
    Jan 22-May 31, 2024
  • Casey Cavanaugh
    Louisiana State University
    Jan 28-May 3, 2024
  • Yanlai Chen
    University of Massachusetts, Dartmouth
    Feb 12-16, 2024; Mar 11-15, 2024; Apr 15-19, 2024
  • Zheng “Leslie” Chen
    University of Massachusetts Dartmouth
    Jan 29-May 3, 2024
  • Yingda Cheng
    Virginia Tech
    Feb 26-Mar 9, 2024
  • Brian Choi
    United States Military Academy
    Apr 15-19, 2024
  • Giovanna Citti
    university of Bologna
    Mar 11-15, 2024
  • Alessandro Contri
    NTNU - Norwegian University of Science and Technology
    Mar 11-15, 2024
  • Melissa De Jesus
    Florida International University
    Apr 15-19, 2024
  • Diego del Castillo-Negrete
    ORNL
    Apr 15-19, 2024
  • Alan Demlow
    Texas A&M University
    Mar 11-15, 2024
  • Amanda Diegel
    Mississippi State University
    Mar 11-15, 2024
  • Wei Ding
    Purdue University
    Apr 15-19, 2024
  • Nadejda Drenska
    Louisiana State University
    Mar 11-15, 2024
  • Vladimir Druskin
    Worcester Polytechnic Institute
    Feb 1-29, 2024
  • Qiang Du
    Columbia University
    Feb 12-16, 2024; Mar 10-13, 2024; Apr 15-19, 2024
  • Rebecca Durst
    University of Pittsburgh
    Feb 12-16, 2024
  • John Evans
    University of Colorado Boulder
    Feb 12-16, 2024
  • Amara Eze
    Morgan State University
    Apr 15-19, 2024
  • Thomas Fai
    Brandeis University
    Mar 11-15, 2024
  • Tyler Fara
    Oregon State University
    Feb 12-16, 2024; Mar 11-15, 2024
  • Patrick Farrell
    University of Oxford
    Feb 4-9, 2024; Feb 12-16, 2024; Mar 11-15, 2024
  • Cynthia Flores
    California State University, Channel Islands
    Apr 15-19, 2024
  • Daniel Fortunato
    Flatiron Institute
    Mar 11-15, 2024
  • Guosheng Fu
    University of Notre Dame
    Feb 11-Apr 30, 2024
  • Padi Fuster Aguilera
    University of Colorado Boulder
    Mar 11-15, 2024
  • Tom Gilat
    Bar-Ilan University
    Mar 11-15, 2024
  • Christian Glusa
    Sandia National Lab
    Apr 12-20, 2024
  • Sônia Gomes
    Universidade Estadual de Campinas
    Jan 29-Apr 26, 2024
  • Hector Gomez
    Purdue University
    Feb 12-16, 2024
  • Tristan Goodwill
    University of Chicago
    Jan 28-Mar 16, 2024
  • Jay Gopalakrishnan
    Portland State University
    Mar 10-22, 2024
  • Yuliya Gorb
    NSF
    Apr 15-19, 2024
  • Boyce Griffith
    University of North Carolina at Chapel Hill
    Feb 12-16, 2024
  • Johnny Guzman
    Brown University
    Jan 29-May 4, 2024
  • Sammy Habach
    University of Rhode Island
    Apr 15-19, 2024
  • Daozhi Han
    State University of New York at Buffalo
    Apr 1-May 3, 2024
  • Zhaolong Han
    University of California San Diego
    Apr 14-20, 2024
  • Yunhui He
    University of Houston
    Feb 12-16, 2024
  • Xiaoming He
    Missouri University of Science and Technology
    Feb 12-16, 2024
  • Qingguo Hong
    Missouri University of Science and Technology
    Apr 14-20, 2024
  • Tamas Horvath
    Oakland University
    Feb 12-16, 2024; Apr 17-24, 2024
  • Kaibo Hu
    University of Edinburgh
    Mar 27-Apr 2, 2024
  • Xiaozhe Hu
    Tufts University
    Jan 28-May 4, 2024
  • Juntao Huang
    Texas Tech University
    Feb 12-16, 2024; Apr 15-19, 2024
  • Xiaokai Huo
    Iowa State University
    Feb 11-16, 2024
  • Olaniyi Iyiola
    Morgan State University
    Apr 14-20, 2024
  • Siavash Jafarzadeh
    Lehigh University
    Apr 15-19, 2024
  • Gabriela Jaramillo
    University of Houston
    Apr 15-19, 2024
  • Ricardo Kabila
    University of Massachusetts Dartmouth
    Feb 20-May 3, 2024; Apr 15-19, 2024
  • Brendan Keith
    Brown University
    Mar 11-15, 2024
  • Arkadz Kirshtein
    Tufts University
    Feb 11-16, 2024; Mar 11-15, 2024
  • Natalia Kopteva
    University of Limerick
    Feb 11-17, 2024; Apr 15-19, 2024
  • Balázs Kovács
    University of Paderborn
    Mar 11-15, 2024
  • Dmitri Kuzmin
    Technische Universität Dortmund
    Feb 12-16, 2024
  • Rongjie Lai
    Purdue University
    Mar 11-15, 2024
  • Hyesuk Lee
    Clemson University
    Feb 12-16, 2024
  • Kang-Ju Lee
    Seoul National University
    Apr 14-20, 2024
  • SANGHYUN LEE
    Florida State University
    Feb 12-16, 2024
  • Seulip Lee
    University of Georgia
    Feb 12-16, 2024
  • Jeonghun Lee
    Baylor University
    Feb 12-16, 2024
  • Satchel Lefebvre
    Tufts
    Feb 12-16, 2024
  • Dmitriy Leykekhman
    University of Connecticut
    Apr 15-19, 2024
  • Jichun Li
    University of Nevada Las Vegas
    Feb 11-17, 2024; Apr 15-20, 2024
  • Xingjie Li
    University of North Carolina at Charlotte
    Feb 12-16, 2024; Mar 11-15, 2024; Apr 15-19, 2024
  • Guang Lin
    Purdue University
    Apr 15-19, 2024
  • Daozhe Lin
    Columbia University
    Apr 14-19, 2024
  • Sijing Liu
    Brown University
    Sep 1, 2023-May 31, 2024
  • Yuan Liu
    Wichita State University
    Jan 31-May 4, 2024
  • WANGBO LUO
    The George Washington University
    Apr 15-19, 2024
  • Erdogan Madenci
    University of Arizona
    Apr 15-19, 2024
  • Rees Madsen
    Northeastern University
    Mar 11-15, 2024
  • Alexandre Madureira
    Laboratório Nacional de Computação Científica
    Mar 19-May 3, 2024
  • Anotida Madzvamuse
    The University of British Columbia
    Feb 12-16, 2024
  • L Mahadevan
    Harvard University
    Mar 11-15, 2024
  • Georg Maierhofer
    University of Cambridge
    Apr 9-20, 2024
  • Frederic Marazzato
    University of Arizona
    Apr 15-19, 2024
  • Kent-Andre Mardal
    University of Oslo
    Feb 8-Apr 18, 2024
  • Marissa Masden
    ICERM
    Sep 6, 2023-May 31, 2024
  • Andre Massing
    Norwegian University of Technology and Science
    Mar 11-15, 2024
  • Praveeni Mathangadeera
    Oregon State University
    Feb 12-16, 2024
  • Leticia Mattos Da Silva
    Massachusetts Institute of Technology
    Mar 11-15, 2024
  • Patrick McDonough
    California State University Channel Islands
    Apr 15-19, 2024
  • Amnon Meir
    Southern Methodist University
    Feb 12-16, 2024; Apr 14-20, 2024
  • Jean-Marie Mirebeau
    ENS Paris-Saclay, CNRS, Université Paris-Saclay
    Mar 11-15, 2024
  • Monica Morales-Hernandez
    Adelphi University
    Feb 12-14, 2024
  • Michael Neilan
    University of Pittsburgh
    Feb 12-16, 2024; Mar 11-15, 2024; Apr 15-19, 2024
  • Nilima Nigam
    Simon Fraser University
    Mar 11-15, 2024
  • Ricardo Nochetto
    University of Maryland
    Jan 28-May 3, 2024
  • Eoghan O'Keefe
    Tufts University
    Feb 12-16, 2024
  • Maxim Olshanskiy
    University of Houston
    Feb 1-Apr 30, 2024
  • Michael Parks
    Oak Ridge National Laboratory
    Apr 15-19, 2024
  • Ravi Patel
    Sandia National Laboratories
    Jan 31-Feb 3, 2024
  • abani patra
    ABANI K PATRA
    Feb 12-16, 2024
  • Malgorzata Peszynska
    Oregon State University
    Feb 12-16, 2024; Mar 11-15, 2024; Apr 15-19, 2024
  • Rodrigo Platte
    Arizona State University
    Apr 15-19, 2024
  • Sara Pollock
    University of Florida
    Jan 28-May 4, 2024
  • Annalisa Quaini
    University of Houston
    Feb 12-16, 2024
  • Petronela Radu
    University of Nebraska, Lincoln
    Apr 15-19, 2024
  • Sivaguru Ravindran
    University of Alabama in Huntsville
    Feb 12-16, 2024; Apr 14-20, 2024
  • Leo Rebholz
    Clemson University
    Jan 28-May 3, 2024
  • Arnold Reusken
    Aachen University
    Mar 11-15, 2024
  • Beatrice Riviere
    Rice University
    Feb 4-17, 2024
  • Michele Ruggeri
    University of Bologna
    Feb 3-17, 2024
  • Ricardo Ruiz-Baier
    Monash University
    Feb 12-16, 2024
  • Riccardo Sacco
    Politecnico di Milano
    Feb 11-16, 2024
  • Abner Salgado
    University of Tennessee
    Jan 28-May 4, 2024
  • Marcus Sarkis
    Worcester Polytechnic Institute
    Jan 29-May 4, 2024
  • Ridgway Scott
    University of Chicago
    Jan 28-May 3, 2024
  • Guglielmo Scovazzi
    Duke University
    Feb 12-16, 2024
  • Pablo Seleson
    Oak Ridge National Laboratory (ORNL)
    Apr 11-16, 2024
  • Jeremy Shahan
    Louisiana State University
    Mar 11-15, 2024
  • Mansur Shakipov
    University of Maryland, College Park
    Mar 11-15, 2024
  • Jinye Shen
    Southwestern University of Finance and Economics
    Apr 15-19, 2024
  • Joshua Siktar
    University of Tennessee-Knoxville
    Apr 15-19, 2024
  • Valeria Simoncini
    Università di Bologna
    Jan 28-Feb 28, 2024; Apr 15-19, 2024
  • Gieri Simonett
    Vanderbilt University
    Mar 11-15, 2024
  • Tatyana Sorokina
    Towson State University
    Mar 11-15, 2024
  • Giselle Sosa Jones
    Oakland University
    Feb 12-16, 2024; Apr 17-24, 2024
  • Reed Spitzer
    Brown University
    Apr 15-19, 2024
  • Monica Stephens
    Spelman College
    Jan 29-May 3, 2024
  • Ari Stern
    Washington University in St. Louis
    Mar 11-15, 2024
  • Zheng Sun
    The University of Alabama
    Jan 29-May 3, 2024
  • Li-yeng Sung
    Louisiana State University
    Jan 30-Apr 30, 2024
  • Xiaochuan Tian
    University of California-San Diego
    Apr 14-20, 2024
  • Giordano Tierra Chica
    University of North Texas
    Jan 31-May 4, 2024
  • Nathaniel Trask
    Sandia National Laboratory
    Feb 12-16, 2024
  • Richard Tsai
    University of Texas
    Mar 3-Apr 18, 2024
  • Tabea Tscherpel
    Technical University of Darmstadt
    Mar 1-25, 2024
  • Chidera Ugbonta
    Tufts University
    Apr 15-19, 2024
  • Odirachukwunma Ugwu
    Morgan State University
    Apr 15-19, 2024
  • Duygu Vargun
    Oak Ridge National Laboratory
    Feb 12-16, 2024
  • Alessandro VENEZIANI
    Emory University
    Feb 12-16, 2024
  • Arjun Vijaywargiya
    University of Notre Dame
    Mar 10-16, 2024
  • Axel Voigt
    Institute of Scientific Computing - Technische Universitat Dresden
    Mar 11-15, 2024
  • Henry von Wahl
    Friedrich Schiller University Jena
    Jan 28-May 4, 2024
  • Johan Waernegaard
    Columbia University
    Mar 11-15, 2024
  • Shawn Walker
    Louisiana State University
    Mar 11-15, 2024
  • Noel Walkington
    Carnegie Mellon University
    Jan 28-May 4, 2024
  • Ying Wang
    University of Oklahoma
    Feb 11-16, 2024; Apr 15-19, 2024
  • Christopher Wang
    Cornell University
    Jan 28-May 4, 2024
  • Yongxing Wang
    University of Leeds
    Mar 11-15, 2024
  • Hong Wang
    University of South Carolina
    Apr 14-20, 2024
  • Xue Wang
    Tufts University
    Feb 12-16, 2024
  • Franziska Weber
    Carnegie Mellon University
    Mar 11-15, 2024
  • Ketahene Gamladdalage Madushi Uththara Wickramasinghe
    Morgan State University
    Apr 15-19, 2024
  • Carol Woodward
    Lawrence Livermore National Laboratory
    Feb 11-16, 2024
  • Bobbie Wu
    University of Massachusetts Lowell
    Mar 11-15, 2024
  • Zhongqin Xue
    Tufts University
    Feb 12-16, 2024
  • Qihao Ye
    University of California, San Diego
    Apr 14-19, 2024
  • Son-Young Yi
    University of Texas at El Paso
    Feb 12-16, 2024
  • Yue Yu
    Lehigh University
    Feb 12-16, 2024; Apr 15-19, 2024
  • Yukun Yue
    University of Wisconsin, Madison
    Jan 29-May 31, 2024
  • Sara Zahedi
    KTH Royal Institute of Technology
    Mar 11-15, 2024
  • Xu Zhang
    Oklahoma State University
    Feb 12-16, 2024
  • Yanzhi Zhang
    Missouri University of Sciences and Technology
    Apr 15-19, 2024
  • Yanxiang Zhao
    George Washington University
    Apr 16-18, 2024
  • Hongkai Zhao
    Duke University
    Mar 11-15, 2024
  • Haoyang Zheng
    Purdue University
    Apr 15-19, 2024
  • Qiao Zhuang
    Worcester Polytechnic Institute
    Feb 12-16, 2024
  • Ludmil Zikatanov
    The Pennsylvania State University
    Apr 15-19, 2024

Visit dates listed on the participant list may be tentative and subject to change without notice.

Semester Schedule

Monday, January 29, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 9:00 am - 4:30 pm EST
    Check In
    11th Floor Collaborative Space
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Tuesday, January 30, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 9:30 - 10:00 am EST
    ICERM Director and Organizer Welcome
    Welcome - 11th Floor Lecture Hall
    • Johnny Guzman, Brown University
    • Brendan Hassett, ICERM/Brown University
    • Maxim Olshanskiy, University of Houston
    • Sara Pollock, University of Florida
    • Abner Salgado, University of Tennessee
    • Valeria Simoncini, Università di Bologna
  • 12:00 - 1:00 pm EST
    Postdoc/Graduate Student Meeting with ICERM Director
    Meeting - 11th Floor Conference Room
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Wednesday, January 31, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 10:00 am - 12:00 pm EST
    Postdoc/ Grad Introductions
    Lightning Talks - 11th Floor Lecture Hall
    • John Carter, Rensselaer Polytechnic Institute
    • Casey Cavanaugh, Louisiana State University
    • Tristan Goodwill, University of Chicago
    • Sijing Liu, Brown University
    • Marissa Masden, ICERM
    • Henry von Wahl, Friedrich Schiller University Jena
    • Christopher Wang, Cornell University
    • Yukun Yue, University of Wisconsin, Madison
  • 2:00 - 3:00 pm EST
    Informal Tea
    Coffee Break - 11th Floor Collaborative Space
Thursday, February 1, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 9:00 - 9:45 am EST
    Introduction and TensorFlow basics
    Tutorial - 11th Floor Lecture Hall
    • Ravi Patel, Sandia National Laboratories
  • 9:45 - 10:15 am EST
    Neural networks I
    Tutorial - 11th Floor Lecture Hall
    • Ravi Patel, Sandia National Laboratories
  • 10:15 - 10:30 am EST
    Break
    Coffee Break
  • 10:30 - 11:30 am EST
    Neural networks II
    Tutorial - 11th Floor Lecture Hall
    • Ravi Patel, Sandia National Laboratories
  • 11:30 am - 1:30 pm EST
    Lunch/Free Time
  • 1:30 - 4:00 pm EST
    Physics informed neural networks and inverse problems
    Tutorial - 11th Floor Lecture Hall
    • Ravi Patel, Sandia National Laboratories
  • 4:00 - 4:30 pm EST
    Coffee Break
    11th Floor Collaborative Space
  • 4:30 - 5:00 pm EST
    Bayesian inference and Gaussian Processes I
    Tutorial - 11th Floor Lecture Hall
    • Ravi Patel, Sandia National Laboratories
Friday, February 2, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 9:00 - 10:15 am EST
    Bayesian Inference and Gaussian Processes II
    Tutorial - 11th Floor Lecture Hall
    • Ravi Patel, Sandia National Laboratories
  • 10:15 - 10:30 am EST
    Break
    Coffee Break
  • 10:30 - 11:30 am EST
    Operator Learning I
    Tutorial - 11th Floor Lecture Hall
    • Ravi Patel, Sandia National Laboratories
  • 11:30 am - 1:30 pm EST
    Lunch/Free Time
  • 1:30 - 3:30 pm EST
    Operator Learning II
    Tutorial - 11th Floor Lecture Hall
    • Ravi Patel, Sandia National Laboratories
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:30 pm EST
    Advanced topics. Future directions. Reproducibility.
    Tutorial - 11th Floor Lecture Hall
  • 4:30 - 5:00 pm EST
    Open Problem Session
    Problem Session - 11th Floor Lecture Hall
    • Ravi Patel, Sandia National Laboratories
Monday, February 5, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 8:30 - 10:30 am EST
    Poisson equation with Dirichlet conditions
    Tutorial - 11th Floor Lecture Hall
    • Patrick Farrell, University of Oxford
    Abstract
    exercise: switch to geometric multigrid
    exercise: switch to high-order
  • 10:30 - 10:45 am EST
    Break
    Coffee Break - 11th Floor Collaborative Space
  • 10:45 am - 12:45 pm EST
    Meshes and meshing
    Tutorial - 11th Floor Lecture Hall
    • Patrick Farrell, University of Oxford
    Abstract
    exercise: adaptive discretisation on L-shaped domain
  • 12:45 - 2:30 pm EST
    Lunch/Free Time
  • 2:30 - 4:30 pm EST
    Poisson with Neumann and Robin conditions
    Tutorial - 11th Floor Lecture Hall
    • Patrick Farrell, University of Oxford
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Tuesday, February 6, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 8:30 - 10:30 am EST
    A foray into transient PDEs
    Tutorial - 11th Floor Lecture Hall
    • Patrick Farrell, University of Oxford
    Abstract
    exercise: Crank-Nicolson for the heat equation
    exercise: implicit RK discretisation of the heat equation
  • 10:30 - 10:45 am EST
    Break
    Coffee Break - 11th Floor Collaborative Space
  • 10:45 am - 12:45 pm EST
    Mixed formulations: the Stokes equations
    Tutorial - 11th Floor Lecture Hall
    • Patrick Farrell, University of Oxford
    Abstract
    exercise: non-Newtonian Stokes
  • 12:45 - 2:30 pm EST
    Lunch/Free Time
  • 1:00 - 2:00 pm EST
    Post Doc/Graduate Student Seminar
    11th Floor Conference Room
  • 2:30 - 4:30 pm EST
    Compressible hyperelasticity
    Tutorial - 11th Floor Lecture Hall
    • Patrick Farrell, University of Oxford
    Abstract
    exercise: write a solver from scratch
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Wednesday, February 7, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 8:30 - 10:30 am EST
    Variational inequalities: the obstacle problem
    Tutorial - 11th Floor Lecture Hall
    • Patrick Farrell, University of Oxford
    Abstract
    exercise: apply a multilevel solver
  • 10:30 - 10:45 am EST
    Break
    Coffee Break - 11th Floor Collaborative Space
  • 10:45 am - 12:45 pm EST
    Eigenvalue problems
    Tutorial - 11th Floor Lecture Hall
    • Patrick Farrell, University of Oxford
    Abstract
    exercise: recreate MATLAB logo
  • 12:45 - 2:30 pm EST
    Lunch/Free Time
  • 2:30 - 4:30 pm EST
    Block preconditioners: Stokes and Navier-Stokes
    Tutorial - 11th Floor Lecture Hall
    • Patrick Farrell, University of Oxford
    Abstract
    exercise: Reynolds-robust solvers for Navier-Stokes
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Thursday, February 8, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:00 - 3:30 pm EST
    Informal discussion on computational linear algebra
    Discussion - 11th Floor Lecture Hall
    • Valeria Simoncini, Università di Bologna
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Friday, February 9, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:30 pm EST
    Discontinuous Galerkin for Moist Air with Implicit Condensation
    11th Floor Lecture Hall
    • Henry von Wahl, Friedrich Schiller University Jena
Monday, February 12, 2024
  • 8:30 - 8:50 am EST
    Check In
    11th Floor Collaborative Space
  • 8:50 - 9:00 am EST
    Welcome
    11th Floor Lecture Hall
    • Brendan Hassett, ICERM/Brown University
  • 9:00 - 9:45 am EST
    Numerical modeling of fluid-structure interaction
    11th Floor Lecture Hall
    • Speaker
    • Martina Bukač, University of Notre Dame
    • Session Chair
    • Sara Pollock, University of Florida
    Abstract
    Fluid-structure interaction problems arise in many applications. In biomedicine, such models are used to describe the interaction between blood and arterial walls. Other applications include geomechanics and aerodynamics. When a deformable structure is porous and allows flow through it, poroelastic models are commonly used to describe its behavior. The numerical simulation of fluid-elastic/poroelastic structure interaction problems has received considerable attention, but still remains a significant challenge in the mathematical and computational sciences. Main difficulties stem from the the intricate multiphysics nature of the problem, and strong nonlinearities. In this talk, we will present some recent advances in numerical modeling of fluid-structure interaction problems, including adaptive, partitioned methods where the domain movement is handled using an Arbitrary Lagragian-Eulerian approach, and a fixed mesh scheme based on the diffuse interface method. We will also present an application of solvers for fluid-structure interaction in the design of a bioartifical pancreas.
  • 10:00 - 10:30 am EST
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EST
    On the design and analysis of property-preserving finite element schemes for hyperbolic problems
    11th Floor Lecture Hall
    • Speaker
    • Dmitri Kuzmin, Technische Universität Dortmund
    • Session Chair
    • Sara Pollock, University of Florida
    Abstract
    This talk presents a family of algebraically constrained finite element schemes for hyperbolic conservation laws. The validity of (generalized) discrete maximum principles is enforced using monolithic convex limiting (MCL), a new flux correction procedure based on representation of spatial semi-discretizations in terms of admissible intermediate states. Semi-discrete entropy stability is enforced using a limiter-based fix. Time integration is performed using explicit or implicit Runge-Kutta methods, which can also be equipped with property-preserving flux limiters. In MCL schemes for nonlinear systems, problem-dependent inequality constraints are imposed on scalar functions of conserved variables to ensure physical and numerical admissibility of approximate solutions. After explaining the design philosophy behind our flux-corrected finite element approximations and showing some numerical examples, we turn to the analysis of consistency and convergence. In particular, we prove a Lax-Wendroff-type theorem for the inequality-constrained semi-discrete problem. A key component of our analysis is the use of a weak estimate on bounded variation, which follows from the semi-discrete entropy stability property of the method under investigation. For the Euler equations of gas dynamics, we prove weak convergence to a dissipative weak solution. The convergence analysis to be presented in this talk is joint work with Maria Lukáčová-Medvid’ová and Philipp Öffner.
  • 11:30 am - 12:15 pm EST
    Coupling mechanics with biochemistry to understand single and collective cell migration: A geometric bulk-surface partial differential equation approach
    11th Floor Lecture Hall
    • Speaker
    • Anotida Madzvamuse, The University of British Columbia
    • Session Chair
    • Sara Pollock, University of Florida
    Abstract
    In this talk I will present a geometric bulk-surface partial differential equations (GBS-PDEs) approach for coupling mechanics with biochemistry to understand mechanisms for single and collective cell migration. The GBS-PDEs are solved efficiently using tailor-made numerical methods depending on the properties of the mathematical models; two novel numerical methods will be presented: (i) the evolving bulk-surface finite element method suitable for solving GBS-PDEs on evolving domains and manifolds for sharp-interface formulations and (ii) the geometric multigrid method suitable for solving PDEs on evolving domains and manifolds using diffuse interface formulations. Experimentally driven inspired applications will be presented, demonstrating the novelty, applicability and generality of this mechanobiochemical modelling approach to studying single and collective cell migration. Cell migration is essential for many physiological and pathological processes. It plays a central role in the development and maintenance of multicellular organisms. Tissue formation during embryonic development, wound healing and immune responses as well as the formation of cancer, all require the orchestrated movement of cells in particular directions to specific locations. Hence, understanding single cell dynamics during movement is critically important in development, biomedicine and biomedical engineering.
  • 12:30 - 2:30 pm EST
    Lunch/Free Time
  • 2:30 - 3:15 pm EST
    Convergence of numerical methods for coupled Cahn-Hilliard and Navier-Stokes equations
    11th Floor Lecture Hall
    • Speaker
    • Beatrice Riviere, Rice University
    • Session Chair
    • Sara Pollock, University of Florida
    Abstract
    Modeling multicomponent flows in porous media is important for many applications relevant to energy and environment. Advances in pore-scale imaging, increasing availability of computational resources, and developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multiphase flow in pore structures feasible. This talk presents recent advances in the discretization of phase-field models for systems of two-phase flows. Spatial discretization is based on the interior penalty discontinuous Galerkin methods. Time discretization utilizes a decoupled splitting approach. Both theory and application of the proposed methods to model flows in porous structures are discussed.
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EST
    New optimized Robin-Robin domain decomposition methods using Krylov solvers for the Stokes-Darcy system
    11th Floor Lecture Hall
    • Speaker
    • Xiaoming He, Missouri University of Science and Technology
    • Session Chair
    • Sara Pollock, University of Florida
    Abstract
    In this presentation, we design optimized Schwarz domain decomposition algorithms to accelerate the Krylov type solution for the Stokes-Darcy system. We use particular solutions of this system on a circular geometry to analyze the iteration operator mode by mode. We introduce a new optimization strategy of the so-called Robin parameters based on a specific linear relation between these parameters, using the min-max and the expectation minimization approaches. Moreover, we use a Krylov solver to deal with the iteration operator and accelerate this new optimized domain decomposition algorithm. Several numerical experiments are provided to validate the effectiveness of this new method.
  • 5:00 - 6:30 pm EST
    Welcome Reception
    Reception - 11th Floor Collaborative Space
Tuesday, February 13, 2024
  • 9:00 - 9:45 am EST
    Immersed methods for fluid-structure interaction
    Virtual
    • Virtual Speaker
    • Boyce Griffith, University of North Carolina at Chapel Hill
    • Session Chair
    • Amnon Meir, Southern Methodist University
    Abstract
    The immersed boundary (IB) method is a framework for modeling systems in which an elastic structure interacts with a viscous incompressible fluid. The fundamental feature of the IB approach to such fluid-structure interaction (FSI) problems is its combination of an Eulerian formulation of the momentum equation and incompressibility constraint with a Lagrangian description of the structural deformations and resultant forces. In conventional IB methods, Eulerian and Lagrangian variables are linked through integral equations with Dirac delta function kernels, and these singular kernels are replaced by regularized delta functions when the equations are discretized for computer simulation. This talk will focus on three related extensions of the IB method. I first detail an IB approach to structural models that use the framework of large-deformation nonlinear elasticity. I will focus on efficient numerical methods that enable finite element structural models in large-scale simulations, with examples focusing on models of the heart and its valves. Next, I will describe an extension of the IB framework to simulate soft material failure using peridynamics, which is a nonlocal structural mechanics formulation. Numerical examples demonstrate constitutive correspondence with classical mechanics for non-failure cases along with essentially grid-independent predictions of fluid-driven soft material failure. Finally, I will introduce a reformulation of the IB large-deformation elasticity framework that enables accurate and efficient fluid-structure coupling through a version of the immersed interface method, which is a sharp-interface IB-type method. Computational examples demonstrate the ability of this methodology to simulate a broad range of fluid-structure mass density ratios without suffering from artificial added mass instabilities, and to facilitate subgrid contact models. I will also present biomedical applications of the methodology, including models of clot capture by inferior vena cava filters.
  • 10:00 - 10:30 am EST
    Coffee Break
    Virtual
  • 10:30 - 11:15 am EST
    AAPicard-Newton solver for Navier-Stokes and related problems
    Virtual
    • Virtual Speaker
    • Leo Rebholz, Clemson University
    • Session Chair
    • Amnon Meir, Southern Methodist University
    Abstract
    We consider the composition of AA-Picard fixed point iteration with Newton iteration, to create a more robust and stable yet still quadratically convergent solver. We analyze for Navier-Stokes in cases of small data (sufficient for uniqueness) and large data. Tests for NSE and other PDEs with this solver show a remarkable ability to converge for larger Reynolds number (NSE), Rayleigh number (Boussinesq), Kerr coefficient and refraction index (nonlinear Helmholtz), and so on.
  • 11:30 am - 12:15 pm EST
    On Reliability and Economics
    Virtual
    • Virtual Speaker
    • Jed Brown, University of Colorado Boulder
    • Session Chair
    • Amnon Meir, Southern Methodist University
    Abstract
    Data structures and algorithms have changed the relative costs, but few production pipelines have internalized the new economics of simulation. For example, matrix-free invert the marginal cost of high order discretizations, enabling large speed-ups for engineering workflows. Meanwhile, there is frequent dispute among practitioners of when to apply linearizations and assumptions on physical regime, when to use structured vs unstructured meshes, and many other important design choices in a simulation tool. For single-physics problems, it is perhaps tractable for analysts to determine (usually a posteriori) when these approximations are valid, but that is more difficult and error-prone for multi-physics problems. We reflect on the computational cost, robustness, and user interface consequences of "simplifying" this decision landscape by embracing fully nonlinear formulations with unstructured meshes and implicit solvers. Via case studies in fluid and structural mechanics, we observe that solvers for more general regimes can have low overhead relative to regime-specific solvers, yet come equipped with diagnostics that provide effective a posteriori indicators of physical regime.
  • 12:30 - 2:30 pm EST
    Lunch/Free Time
  • 2:30 - 3:15 pm EST
    Fluid-poroelastic structure interaction
    Virtual
    • Speaker
    • Suncica Canic, University of California, Berkeley
    • Session Chair
    • Amnon Meir, Southern Methodist University
    Abstract
    We will discuss some recent results on fluid-poroelastic structrure interaction between multilayered poroelastic media and viscous, incompressible fluids.
Wednesday, February 14, 2024
  • 9:00 - 9:45 am EST
    Multiscale/Multiphysics Modeling and Simulation in Ophthalmology
    11th Floor Lecture Hall
    • Virtual Speaker
    • Riccardo Sacco, Politecnico di Milano
    • Session Chair
    • Hyesuk Lee, Clemson University
    Abstract
    Glaucoma is a multifactorial ocular neuropathology representing the second major cause of irreversible blindness. Elevated intraocular pressure (IOP) is an established risk factor of glaucoma determined by aqueous humor dynamics (AHDyn), the balance among production (Pr), diffusion (Diff) and drainage (Dr) of aqueous humor (AH), a watery transparent fluid including electrolytes and low protein concentration. Reducing AH-Pr and/or increasing AH-Dr are possible approaches to reduce IOP. In this talk we illustrate a multiscale/multiphysics approach to develop a computational virtual laboratory (CVL) for the simulation of AHDyn based on a 3D-to-0D reduction of (1) 3D Velocity-Extended Poisson-Nernst-Planck PDE system to model AH-Pr; (2) 3D diffusion bulk flow to model AH-Diff; (3) 3D poroelastic PDE system to model AH-Dr. Model variables are the compartment values of electric potential, ion molar densities and fluid pressure and are numerically determined by a fixed-point iteration which transforms AHDyn simulation into the successive solution of two nonlinear systems of algebraic equations, representing mass balance in AH-Pr and in AH-Diff + AH-Dr, respectively. Computational tests suggest that Na+/K+ pump and TM/Uv hydraulic facilities are the main biomarkers of a pathological increase in IOP. These results support the potential use of a CVL to assist and optimize the design of IOP lowering medications.
  • 10:00 - 10:30 am EST
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EST
    Multiphysics at multiple scales for coupled [TpHM] processes in permafrost soils
    11th Floor Lecture Hall
    • Speaker
    • Malgorzata Peszynska, Oregon State University
    • Session Chair
    • Hyesuk Lee, Clemson University
    Abstract
    In this joint work with many students and collaborators we describe robust and conservative computational schemes for coupled process of flow, deformation, and energy with phase change (TpHM) in the soils in permafrost regions. The models present challenges due to the free boundary of freezing/thawing, strong dependence of constitutive parameters on the micro-physics of TpHM, disparate time scales, and micro- and macro heterogeneity. We also discuss how to get the data for the Darcy scale [TpH] ad [HM] models from the models at the pore-scale by computational upscaling.
  • 11:30 am - 12:15 pm EST
    Multiphysics problems related to brain clearance, sleep and dementia
    11th Floor Lecture Hall
    • Speaker
    • Kent-Andre Mardal, University of Oslo
    • Session Chair
    • Hyesuk Lee, Clemson University
    Abstract
    Recent theories suggest that a fundamental reason for sleep is simply clearance of metabolic waste produced during the activities of the day. In this talk we will present multi-physics problems and numerical schemes that target these applications. In particular, we will be lead from basic applications of neuroscience into multi-physics problems involving Stokes, Biot and fractional solvers at the brain-fluid interface.
  • 12:25 - 12:30 pm EST
    Group Photo (Immediately After Talk)
    11th Floor Lecture Hall
  • 12:30 - 2:30 pm EST
    Poster Session Lunch
    Poster Session - 10th Floor Collaborative Space
  • 2:30 - 3:15 pm EST
    Direct van der Waals Simulation (DVS): Towards Predictive Simulations of Cavitation and Boiling
    11th Floor Lecture Hall
    • Speaker
    • Hector Gomez, Purdue University
    • Session Chair
    • Hyesuk Lee, Clemson University
    Abstract
    Cavitating flows are ubiquitous in engineering and science. Despite their significance, a number of fundamental problems remain open; and our ability to make quantitative predictions is very limited. The Navier-Stokes-Korteweg equations constitute a fundamental model of cavitation, which has potential for predictive computations of liquid-vapor flows, including cavitation inception —one of the most elusive aspects of cavitation. However, numerical simulation of the Navier-Stokes-Korteweg equations is very challenging, and state of the art simulations are limited to very small Reynolds numbers, open flows (no walls), and in most cases, micrometer length scales. The computational challenges emerge from, at least, (a) the dispersive nature of the solutions to the equations, (b) a complicated eigenstructure of the isentropic form of the equations, which limits the use of standard CFD techniques, and (c) the need to resolve the liquid-vapor interface, which without special treatment, has a thickness in the order of nanometers. Here, we present Direct van der Waals simulation (DVS), a new approach that permits, for the first time as far as we are aware, large-scale simulations of wall-bounded flows with large Reynolds numbers. The proposed discretization scheme is a residual-based approach that emanates from the dispersive nature of the equations and outperforms standard stabilization schemes for advection-dominated problems. We feel that this work opens possibilities for predictive simulations of cavitation.
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EST
    A data-driven exterior calculus
    11th Floor Lecture Hall
    • Speaker
    • Nathaniel Trask, Sandia National Laboratory
    • Session Chair
    • Hyesuk Lee, Clemson University
    Abstract
    Despite the recent flurry of work employing machine learning to develop surrogate models to accelerate scientific computation, the "black-box" underpinnings of current techniques fail to provide the verification and validation guarantees provided by modern finite element methods. In this talk we present a data-driven finite element exterior calculus for developing reduced-order models of multiphysics systems when the governing equations are either unknown or require closure. The framework employs deep learning architectures typically used for logistic classification to construct a trainable partition of unity which provides notions of control volumes with associated boundary operators. This alternative to a traditional finite element mesh is fully differentiable and allows construction of a discrete de Rham complex with a corresponding Hodge theory. We demonstrate how models may be obtained with the same robustness guarantees as traditional mixed finite element discretization, with deep connections to contemporary techniques in graph neural networks. For applications developing digital twins where surrogates are intended to support real time data assimilation and optimal control, we further develop the framework to support Bayesian optimization of unknown physics on the underlying adjacency matrices of the chain complex. By framing the learning of fluxes via an optimal recovery problem with a computationally tractable posterior distribution, we are able to develop models with intrinsic representations of epistemic uncertainty.
Thursday, February 15, 2024
  • 9:00 - 9:45 am EST
    The Role of Multiphysics Modeling in the Design of Coronary Stents
    11th Floor Lecture Hall
    • Speaker
    • Alessandro Veneziani, Emory University
    • Session Chair
    • Noel Walkington, Carnegie Mellon University
    Abstract
    Since their introduction in the Eighties, coronary stents have undergone significant design improvements, making them a critical tool for treating severe obstructions. From original Bare-Metal Stents (BMS) to Drug Eluting Stents (DES) to the most recent experience of Bioresorbable Stents, the design of these scaffolds was minimally supported by mathematical tools. The patient-specific quantitative analysis of stented coronaries is a difficult task for the variety of complex morphologies left by the stent deployment. Therefore, this type of analysis was limited to a minimal number of patients, not compatible with clinical trials. On the other hand, the development and the failure of Brioresorbable Stents clearly pointed out the importance of rigorous quantitative tools in the design of next-generation scaffolds. In this talk, we will present recent results in investigating coronary stents based on Applied Mathematics (as opposed to traditional animal models). We will consider in detail (i) the modeling of the elution in a multidomain problem solved by iterative substructuring methods involving simultaneously the lumen, the wall, and the struts of the stents; (2) the impact of the struts on the wall shear stress of a significant number of patients; (3) the consequent role of shape optimization and model order reduction in the design of scaffolds. This journey through a sophisticated combination of data and models will pinpoint the critical role of applied mathematics and scientific computing not only for a basic understanding of the biomechanics of stents but also for the clinical routine and the design of more performing prostheses.
  • 10:00 - 10:30 am EST
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EST
    Domain Agnostic Neural Operators for Multiphysics Problems
    11th Floor Lecture Hall
    • Speaker
    • Yue Yu, Lehigh University
    • Session Chair
    • Noel Walkington, Carnegie Mellon University
    Abstract
    Over the past several decades, physics-based Partial Differential Equations (PDEs) have been the cornerstone for modeling multiphysics problems. Traditional numerical methods have been employed to solve these PDEs and various approaches have been proposed to capture the multiphysics interfaces. However, their accuracy and computational feasibility can be compromised when dealing with unknown governing laws or complex interface geometries, such as in the crack propagation, fluid—structure interaction, and heterogeneous material design problems. In this talk, we develop to use data-driven modeling approaches to learn the hidden physics, capture irregular geometries, and provide accelerated predictions. In particular, we introduce domain agnostic Fourier neural operator (DAFNO), which learns the surrogate mapping between loading conditions and the corresponding physical responses with irregular geometries and evolving domains. The key idea is to incorporate a smoothed characteristic function in the integral layer architecture of neural operators, and leverage FFT to achieve rapid computations for evaluating these integrals, in such a way that the geometric information is explicitly encoded in the architecture. Once trained, DAFNO can provide efficient predictions for physical problems under unseen loading scenarios and evolving domain geometries, which makes it especially suitable to handle the complex interfacial problems in multiphysics modeling. To illustrate the applicability of DAFNO in multiphysics problems, we show three examples. Firstly, we consider a brittle material crack propagation problem which features complex domains with topology changes. Then, in the second example we further consider the corrosion induced cracking in reinforced concrete, which is a multiphysics system involving the interactions between diffusion, chemical reaction, mechanical strain, and crack fields. Last but not least, we show that DAFNO can act as an efficient surrogate for the inverse microstructure design of multifunctional metamaterials. These examples highlight the features of DAFNOs in its generalizability, flexibility, and efficiency.
  • 11:30 am - 12:15 pm EST
    The Shifted Boundary Method: An embedded approach for computational mechanics
    11th Floor Lecture Hall
    • Speaker
    • Guglielmo Scovazzi, Duke University
    • Session Chair
    • Noel Walkington, Carnegie Mellon University
    Abstract
    Embedded/immersed/unfitted boundary methods obviate the need for continual re-meshing in many applications involving rapid prototyping and design. Unfortunately, many finite element embedded boundary methods are also difficult to implement due to the need to perform complex cell cutting operations at boundaries, and the consequences that these operations may have on the overall conditioning of the ensuing algebraic problems. We present a new, stable, and simple embedded boundary method, named Shifted Boundary Method (SBM), which eliminates the need to perform cell cutting. Boundary conditions are imposed on a surrogate discrete boundary, lying on the interior of the true boundary interface. We then construct appropriate field extension operators by way of Taylor expansions, with the purpose of preserving accuracy when imposing the boundary conditions. We demonstrate the SBM on large-scale solid and fracture mechanics problems; thermoelasticity problems; porous media flow problems; incompressible flow problems governed by the Navier-Stokes equations (also including free surfaces); and problems governed by hyperbolic conservation laws.
  • 12:30 - 2:30 pm EST
    Lunch: Classical theory vs machine learning in education
    Working Lunch - 11th Floor Collaborative Space
  • 2:30 - 3:15 pm EST
    A FEM for a phase-field model of two-phase incompressible surface flow with electrostatic interaction
    11th Floor Lecture Hall
    • Speaker
    • Annalisa Quaini, University of Houston
    • Session Chair
    • Noel Walkington, Carnegie Mellon University
    Abstract
    We consider a thermodynamically consistent phase-field model of a two-phase flow of incompressible viscous fluids with electrostatic interaction. The model allows for a nonlinear dependence of the fluid density on the phase-field order parameter. Driven by applications in biomembrane studies, the model is written for tangential flows of fluids constrained to a surface and consists of (surface) Navier–Stokes–Cahn–Hilliard type equations. We apply an unfitted finite element method to discretize the system and introduce a fully discrete time-stepping scheme with the following properties: (i) the scheme decouples the fluid and phase-field equation solvers at each time step, (ii) the resulting two algebraic systems are linear, and (iii) the numerical solution satisfies the same stability bound as the solution of the original system under some restrictions on the discretization parameters. We provide numerical examples to demonstrate the stability, accuracy, and overall efficiency of the approach and provide validation against experimental data.
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EST
    Positivity-preserving discretisations in general meshes
    11th Floor Lecture Hall
    • Speaker
    • Gabriel Barrenechea, University of Strathclyde
    • Session Chair
    • Noel Walkington, Carnegie Mellon University
    Abstract
    In this talk I will present a method that enforces bound-preservation (at the degrees of freedom) of the discrete solution (recently presented in [1]). The method is built by first defining an algebraic projection onto the convex closed set of finite element functions that satisfy the bounds given by the solution of the PDE. Then, this projection is hardwired into the definition of the method by writing a discrete problem posed for this projected part of the solution. Since this process is done independently of the shape of the basis functions, and no result on the resulting finite element matrix is used, this process guarantees bound-preservation independently of the underlying mesh. The core of the talk will be devoted to explaining the main idea in the context of linear (and nonlinear) reaction-diffusion equations. Then, I will explain the main difficulties encountered when extending this method to convection-diffusion equations, and to a finite element method defined in polytopal meshes. The results in this talk have been carried out in collaboration with Abdolreza Amiri (Strathclyde, UK), Emmanuil Geourgoulis (Heriot-Watt, UK and Athens, Greece), Tristan Pryer (Bath, UK), and Andreas Veeser (Milan, Italy). References 1. G.R. Barrenechea, E. Georgoulis, T. Pryer, and A. Veeser, A nodally bound-preserving finite element method. arXiv:2304.01067, IMA Journal on Numerical Analysis, to appear.
Friday, February 16, 2024
  • 9:00 - 9:45 am EST
    Quantum Digital Twins - a numerical methodist’s adventure in the land of quantum computers
    11th Floor Lecture Hall
    • Speaker
    • Daniel Appelö, Virginia Tech
    • Session Chair
    • Valeria Simoncini, Università di Bologna
    Abstract
    In this talk I will introducing the most basic concepts in quantum computing and describe one type of quantum computing hardware (a transmon) and how it is modeled. We will then outline the computationally challenging tasks that are needed for making a quantum computer run and introduce numerical methods tailored especially for these tasks. Time permitting I will take you on a comprehensive journey through a real-world example involving characterization, control, and experimental validation, showcasing our experiences with a qutrit device within the Lawrence Livermore QUDIT testbed.
  • 10:00 - 10:30 am EST
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EST
    Monolithic and Partitioned FEM for FSI: ALE divergence-free HDG fluid solver + TDNNS structural solver
    11th Floor Lecture Hall
    • Speaker
    • Guosheng Fu, University of Notre Dame
    • Session Chair
    • Valeria Simoncini, Università di Bologna
    Abstract
    We present novel (high-order) finite element schemes for the fluid-structure interaction (FSI) problem based on an arbitrary Lagrangian-Eulerian divergence-free hybridizable discontinuous Gakerkin (ALE divergence-free HDG) incompressible flow solver, a Tangential-DisplacementNormal-Normal-Stress (TDNNS) nonlinear elasticity solver, and a generalized Robin interface condition treatment. Temporal discretization is performed using the high-order backward difference formulas (BDFs). Both monolithic and strongly coupled partitioned fully discrete schemes are obtained. Numerical convergence studies are performed for the flow and elasticity solvers, and the coupled FSI solver, which verify the high-order space-time convergence of the proposed schemes. Numerical results on classical two dimensional benchmark problems also showed good performance of our proposed methods.
  • 11:30 am - 12:15 pm EST
    Mixed methods for the coupled Stokes/Poisson-Nernst-Planck equations in Banach spaces
    11th Floor Lecture Hall
    • Speaker
    • Ricardo Ruiz-Baier, Monash University
    • Session Chair
    • Valeria Simoncini, Università di Bologna
    Abstract
    I will discuss a Banach spaces-based framework and new mixed finite element methods for the numerical solution of the coupled Stokes and Poisson-Nerns-Planck equations (a nonlinear model describing the dynamics of electrically charged incompressible fluids). The pseudostress tensor, the electric field (rescaled gradient of the potential) and total ionic fluxes are used as new mixed unknowns. The resulting fully mixed variational formulation consists of two saddle-point problems, each one with nonlinear source terms depending on the remaining unknowns, and a perturbed saddle-point problem with linear source terms, which is in turn additionally perturbed by a bilinear form. The well-posedness of the continuous formulation is a consequence of a fixed-point strategy in combination with the Banach theorem, the Babuska-Brezzi theory, the solvability of abstract perturbed saddle-point problems, and the Banach-Necas-Babuska theorem. An analogous approach (but using now both the Brouwer and Banach theorems and stability conditions on arbitrary FE subspaces) is employed at the discrete level. A priori error estimates are derived, and examples of discrete spaces that fit the theory, include, e.g., Raviart--Thomas elements along with piecewise polynomials. Finally, several numerical experiments confirm the theoretical error bounds and illustrate the balance-preserving properties and applicability of the proposed family of methods. This talk is based on joint work with Claudio I. Correa and Gabriel N. Gatica (from CI2MA, Concepcion).
  • 12:30 - 2:30 pm EST
    Lunch: Networking
    Working Lunch - 11th Floor Collaborative Space
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Tuesday, February 20, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 12:00 - 12:30 pm EST
    de Rham complex
    Post Doc/Graduate Student Seminar - 11th Floor Conference Room
    • Casey Cavanaugh, Louisiana State University
  • 12:30 - 1:00 pm EST
    Potential theory
    Post Doc/Graduate Student Seminar - 11th Floor Conference Room
    • Tristan Goodwill, University of Chicago
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Wednesday, February 21, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 11:00 am - 12:00 pm EST
    Data-driven computation of the interior solutions of LTI PDE problems with unknown coefficients via network realizations of reduced order models
    11th Floor Lecture Hall
    • Vladimir Druskin, Worcester Polytechnic Institute
    Abstract
    We consider computation of the solutions of linear time-invariant hyperbolic PDEs with unknown coefficients from the measurements of their multi-input/multi-output (MIMO) transfer functions with limited number of inputs and outputs. Such problems are paramount in remote sensing and other “noninvasive problems”, e.g., radar imaging, seismic exploration and medical applications, where measurements are not available in the interior problem. We first compute an equivalent network approximation using the interpretation on the Lanczos algorithm via Stieltjes continued fraction, and then compute the state solution by embedding this approximation in the underlying PDE using the finite-difference Gaussian quadratures. We show application of this approach to nondestructive acoustic testing and SAR (Synthetic Aperture Radar) imaging . Contributors to different stages of this long-term project have been Jorn Zimmerling, Mikhail Zaslavsky, Shari Moskow, Alexander Mamonov, Liliana Borcea, Elena Cherkaev and Justin Baker.
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Thursday, February 22, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 12:00 - 1:00 pm EST
    Advances in Flight Simulation and Flow Instability
    11th Floor Lecture Hall
    • Ridgway Scott, University of Chicago
    Abstract
    A new era in flight is emerging that requires a moreeffective simulation strategy. Many modes of transportation are being developed industrially, including air-taxi drones and ground-effect transport. We describe an approach to simulating flight that is based on instabilities in flow and provides a new view of turbulence based on chaotic dynamics of computed flow profiles. The method we use is the Reynolds-Orr definition of instability that is more general than what is commonly used to define flow instability. We show that our results correlate well with what can be observed by both experiment and direct numerical simulation.
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Friday, February 23, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 9:30 - 10:30 am EST
    Ethics I
    Professional Development - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Monday, February 26, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Tuesday, February 27, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 12:00 - 1:00 pm EST
    Convection-dominated equations
    Post Doc/Graduate Student Seminar - 11th Floor Conference Room
    • Casey Cavanaugh, Louisiana State University
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Wednesday, February 28, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 12:00 - 1:00 pm EST
    Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations
    11th Floor Lecture Hall
    • Yingda Cheng, Virginia Tech
    Abstract
    In this talk, we present a new class of implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using a base implicit solve for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. We prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Thursday, February 29, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 12:00 - 1:00 pm EST
    Fundamentals of (simplicial) Mesh Generation
    11th Floor Lecture Hall
    • Noel Walkington, Carnegie Mellon University
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Friday, March 1, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 9:30 - 10:30 am EST
    Ethics II
    Professional Development - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Monday, March 4, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Tuesday, March 5, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 12:00 - 12:30 pm EST
    Discontinuous Galerkin method
    Post Doc/Graduate Student Seminar - 11th Floor Conference Room
    • Henry von Wahl, Friedrich Schiller University Jena
  • 12:30 - 1:00 pm EST
    Surface PDEs
    Post Doc/Graduate Student Seminar - 11th Floor Conference Room
    • Tristan Goodwill, University of Chicago
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Wednesday, March 6, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Thursday, March 7, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 11:00 am - 12:00 pm EST
    Runge--Kutta discontinuous Galerkin methods beyond the method of lines
    11th Floor Lecture Hall
    • Zheng Sun, The University of Alabama
    Abstract
    In the common practice of the method-of-lines approach for discretizing a time-dependent partial differential equation (PDE), people first apply spatial discretization to convert the PDE into an ordinary differential equation system. Subsequently, a time integrator is used to discretize the time variable. When a multi-stage Runge-Kutta (RK) method is used for time integration, by default, the same spatial operator is used at all RK stages. But what if one allows different spatial operators at different stages? In this talk, we present two of our recent explorations on blending different stage operators in RK discontinuous Galerkin (DG) methods for solving hyperbolic conservation laws. In our first work, we mix the DG operator with the local derivative operator, yielding an RKDG method featuring compact stencils and simple boundary treatment. In our second work, we mix the DG operators with polynomials of degrees k and k-1, and the resulting method may allow larger time step sizes and fewer floating-point operations per time step.
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Friday, March 8, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 9:30 - 10:30 am EST
    Job Applications
    Professional Development - 11th Floor Lecture Hall
  • 11:00 am - 12:00 pm EST
    Fast Integral Equation Method for Surface PDEs
    11th Floor Lecture Hall
    • Tristan Goodwill, University of Chicago
  • 3:30 - 4:00 pm EST
    Coffee Break
    11th Floor Collaborative Space
Monday, March 11, 2024
  • 8:30 - 8:50 am EDT
    Check In
    11th Floor Collaborative Space
  • 8:50 - 9:00 am EDT
    Welcome
    11th Floor Lecture Hall
    • Brendan Hassett, ICERM/Brown University
  • 9:00 - 9:45 am EDT
    A nonlinear least-squares convexity enforcing finite element method for the Monge-Ampere equation
    11th Floor Lecture Hall
    • Speaker
    • Susanne Brenner, Louisiana State University
    • Session Chair
    • Michael Neilan, University of Pittsburgh
    Abstract
    We present a nonlinear least-squares finite element method for computing the smooth convex solutions of the Dirichlet boundary value problem of the Monge-Ampere equation on smooth strictly convex planar domains. It is based on an isoparametric finite element space with exotic degrees of freedom that can enforce the convexity of the approximate solutions.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    The Second Boundary Value Problem for a Discrete Monge–Ampere Equation
    11th Floor Lecture Hall
    • Speaker
    • Gerard Awanou, University of Illinois, Chicago
    • Session Chair
    • Michael Neilan, University of Pittsburgh
    Abstract
    We propose a discretization of the second boundary condition for the Monge–Ampere equation arising in geometric optics and optimal transport. The discretization we propose is the natural generalization of the popular Oliker–Prussner method proposed in 1988. For the discretization of the differential operator, we use a discrete analogue of the subdifferential. Existence and stability of the solutions to the discrete problem are established. Convergence results to the continuous problem are given.
  • 11:30 am - 12:15 pm EDT
    A Volumetric Approach to Monge's Optimal Transport on Surfaces
    11th Floor Lecture Hall
    • Speaker
    • Richard Tsai, University of Texas
    • Session Chair
    • Michael Neilan, University of Pittsburgh
    Abstract
    In this talk, we present a novel approach for solving the Monge-Ampere (MA) equation defined on a sphere. Specifically, we extend the MA equation on a sphere to a narrowband around the sphere by formulating an equivalent optimal transport problem. We demonstrate that the extended MA equation can be solved using existing algorithms developed for the MA equation on Euclidean space, making the resulting algorithm simple and easy to implement. Our approach provides a useful tool for solving problems that involve the MA equation defined on or near a sphere, which has a wide range of applications in fields such as computer graphics, image processing, and fluid dynamics.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    Discretizations of anisotropic PDEs using Voronoi's reduction of quadratic forms.
    11th Floor Lecture Hall
    • Speaker
    • Jean-Marie Mirebeau, ENS Paris-Saclay, CNRS, Université Paris-Saclay
    • Session Chair
    • Michael Neilan, University of Pittsburgh
    Abstract
    Anisotropy, which refers to the existence of preferred direction in a domain, is a source of difficulty in the discretization of partial differential equations (PDEs). For instance, monotone discretization schemes for anisotropic PDEs cannot be strictly local, but need to use wide stencils. When the PDE is discretized over a Cartesian grid domain, one can often leverage a matrix decomposition technique known as Voronoi's first reduction, which helps in finding the best possible compromises in the design of anisotropic finite difference schemes. I will describe this tool and its application to monotone discretizations of Hamilton-Jacobi-Bellman PDEs, as well as a recent extensions to the elastic wave equation in a fully general anisotropic medium.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    Controlling growth and form: mineral, vegetable and animal
    11th Floor Lecture Hall
    • Speaker
    • L Mahadevan, Harvard University
    • Session Chair
    • Michael Neilan, University of Pittsburgh
    Abstract
    Shape enables and constrains function across scales, in living and non-living systems. Following a brief introduction to morphogenesis in biology that rapidly touches on how stems, leaves, flowers, bodies, guts, beaks and brains get their shape, I will switch to the inverse problem of how to program and design shape using 3 examples: chemical precipitation, 4d printing and origami/kirigami. Along the way, I will indicate how these pan-disciplinary problems provide a plethora of questions in mathematics, physics and biology, with potential implications for technology.
  • 5:00 - 6:30 pm EDT
    Welcome Reception
    Reception - 11th Floor Collaborative Space
Tuesday, March 12, 2024
  • 9:00 - 9:45 am EDT
    Computational Mean-field Games: From Conventional Methods to Deep Generative Models
    11th Floor Lecture Hall
    • Speaker
    • Rongjie Lai, Purdue University
    • Session Chair
    • Maxim Olshanskiy, University of Houston
    Abstract
    Mean field game (MFG) problems study how a large number of similar rational agents make strategic movements to minimize their costs. They have recently gained great attention due to their connection to various problems, including optimal transport, gradient flow, deep generative models, as well as reinforcement learning. In this talk, I will elaborate our recent computational efforts on MFGs. I will start with a low-dimensional setting, employing conventional discretization and optimization methods, delving into the convergence results of our proposed approach. Afterwards, I will extend my discussion to high-dimensional problems by bridging the trajectory representation of MFG with a special type of deep generative model—normalizing flows. This connection not only helps solve high-dimensional MFGs but also provides a way to improve the robustness of normalizing flows. If time permits, I will further address the extension of these methods to Riemannian manifolds in low-dimensional and higher-dimensional setting, respectively.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    Semi-Supervised Learning with the p-Laplacian in Geometric Methods in Machine Learning and Data Analysis
    11th Floor Lecture Hall
    • Speaker
    • Nadejda Drenska, Louisiana State University
    • Session Chair
    • Maxim Olshanskiy, University of Houston
    Abstract
    The field of semi-supervised learning involves learning from both labeled and unlabeled data. By exploiting the structure of the unlabeled data, such as its geometric or topological properties, semi-supervised classifiers can obtain good performance with far fewer labels than are required in fully supervised learning (when classifiers learn only from labeled data). A semi-supervised approach is necessary when labels are very expensive to obtain, as is the case in a majority of classification applications, such as website classification, text recognition, protein sequencing, medical imaging, natural language processing. In this talk we apply p-Laplacian regularization to cases of very low labeling rate; in such applications this approach classifies properly when the standard Laplacian regularization does not. Using the two-player stochastic game interpretation of the p-Laplacian, we prove asymptotic consistency of p-Laplacian regularized semi-supervised learning, thus justifying the utility of the p-Laplacian.
    This is joint work with Jeff Calder.
  • 11:30 am - 12:15 pm EDT
    Solving PDEs on point clouds with applications to shape analysis
    11th Floor Lecture Hall
    • Speaker
    • Hongkai Zhao, Duke University
    • Session Chair
    • Maxim Olshanskiy, University of Houston
    Abstract
    Using point clouds is the most natural and ubiquitous way of representing geometry and data in 3D and higher. In this talk, I will present a framework of solving geometric PDEs directly on point clouds based on local tangent space parametrization. Then I will talk about some applications in shape analysis for point clouds. Unlike images, which have a canonical form of representation as functions defined on a uniform grid on a rectangular domain, surfaces and manifolds in 3D and higher are geometric objects that do not have a canonical or natural form of representation or global parametrization. Moreover, their embeddings in the ambient space are not intrinsic. We show how geometric PDEs can be used to “connect the dots” and extract intrinsic geometric information for the underlying point clouds for shape analysis.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    Finite element methods for ill-posed interface problems
    11th Floor Lecture Hall
    • Speaker
    • Erik Burman, University College London
    • Session Chair
    • Maxim Olshanskiy, University of Houston
    Abstract
    In this talk we will consider recent advances on the approximation of second order elliptic problems with interfaces that have poor, non-standard stability, or are ill-posed. Such problems arise in a multitude of applications for example in seismic inversion problems or the design of meta materials. As a model problem we will consider the classical ill-posed problem of unique continuation in a heterogeneous environment. First we will discuss primal-dual stabilized finite elements for the homogeneous case and recall recent results on the accuracy and optimality of such methods. Then we will show how the method can be modified to handle internal interfaces using an unfitted finite element method. We will report error estimates for this method and discuss how to handle the destabilizing effect of error in the geometrical data. Finally we will show how the ideas can be applied to so-called sign changing materials, where the coefficient of the diffusion operator is of different sign in different subdomain. The accurate approximation of wave propagation in such materials are important for the design of meta-materials.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    Divergence preserving cut finite element methods
    11th Floor Lecture Hall
    • Speaker
    • Sara Zahedi, KTH Royal Institute of Technology
    • Session Chair
    • Maxim Olshanskiy, University of Houston
    Abstract
    I will give an introduction to Cut Finite Element Methods (CutFEM) for interface problems and present our recent development that results in pointwise divergence-free velocity approximations of incompressible flows.
Wednesday, March 13, 2024
  • 9:00 - 9:45 am EDT
    Navier-Stokes equations on surfaces: Analysis and numerical simulations
    11th Floor Lecture Hall
    • Speaker
    • Arnold Reusken, Aachen University
    • Session Chair
    • Ricardo Nochetto, University of Maryland
    Abstract
    In this presentation we consider a Navier-Stokes type system, posed on a smooth closed stationary or evolving two-dimensional surface embedded in three dimensional space. We briefly address modeling aspects related to this system. We introduce the so-called tangential surface Navier-Stokes equations and discuss a well-posed weak variational formulation of this PDE system that forms the basis for finite element discretization methods. Furthermore we explain the basic ideas of an unfitted finite element method, known as TraceFEM, that is used in our numerical simulation of the tangential surface Navier-Stokes system. Results of numerical experiments with this method are presented that illustrate how lateral flows are induced by smooth deformations of a material surface.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    Nodal FEM for the surface Stokes problem
    11th Floor Lecture Hall
    • Speaker
    • Alan Demlow, Texas A&M University
    • Session Chair
    • Ricardo Nochetto, University of Maryland
    Abstract
    The Stokes and Navier-Stokes problems formulated on surfaces present a number of challenges distinct from those encountered for the corresponding Euclidean equations. In the context of numerical methods, these include the inability to formulate standard surface finite element velocity fields which are simultaneously continuous (H1-conforming) and tangential to the surface. In this talk we will give an overview of various finite element methods that have been derived for the surface Stokes problem, along with their advantages and drawbacks. We will then present a surface counterpart to the Euclidean MINI element which is the first FEM for the surface Stokes problem which does not require any penalization. Finally, we will briefly discuss extension to other nodal Stokes FEM such as Taylor-Hood elements. This is joint work with Michael Neilan.
  • 11:30 am - 12:15 pm EDT
    Fluid flow on surfaces
    11th Floor Lecture Hall
    • Speaker
    • Gieri Simonett, Vanderbilt University
    • Session Chair
    • Ricardo Nochetto, University of Maryland
    Abstract
    I will consider the motion of an incompressible viscous fluid on compact manifolds (with or without boundary). Local in time well-posedness is established in the framework of $L_p$-$L_q$ maximal regularity for initial values in critical spaces. It will be shown that the set of equilibria consists exactly of the Killing vector fields. Each equilibrium is stable and any solution starting close to an equilibrium converges at an exponential rate to a (possibly different) equilibrium. In case the surface is two-dimensional, it will be shown that any solution with divergence free initial value in $L_2$ exists globally and converges to an equilibrium.
  • 12:25 - 12:30 pm EDT
    Group Photo (Immediately After Talk)
    11th Floor Lecture Hall
  • 12:30 - 2:30 pm EDT
    Mentoring Discussion for Early Career Researchers and Students (Organized by Susanne Brenner, Sara Pollock, Michael Neilan)
    Lunch/Free Time - 11th Floor Collaborative Space
  • 2:30 - 3:15 pm EDT
    Two-phase flows on deformable surfaces
    11th Floor Lecture Hall
    • Speaker
    • Axel Voigt, Institute of Scientific Computing - Technische Universitat Dresden
    • Session Chair
    • Ricardo Nochetto, University of Maryland
    Abstract
    We extend the concept of fluid deformable surfaces to two-phase flows. The equations are derived by a Largange-d'Alembert principle and solved by surface finite elements. We demonstrate the huge possibilities of shape evolutions resulting from the strong interplay of phase-dependent bending properties, the line tension and the surface viscosity.
  • 3:30 - 5:00 pm EDT
    Poster Session/ Coffee Break
    Poster Session - 10th Floor Collaborative Space
Thursday, March 14, 2024
  • 9:00 - 9:45 am EDT
    Finite Element Methods For Curvature
    11th Floor Lecture Hall
    • Speaker
    • Shawn Walker, Louisiana State University
    • Session Chair
    • Axel Voigt, Institute of Scientific Computing - Technische Universitat Dresden
    Abstract
    This talk presents some recent advances in extending the classic Hellan--Herrmann--Johnson (HHJ) finite element to surfaces for approximation of bending problems and computing curvature. We give a review of the surface version of the HHJ method which leads to a convergent method to solve the surface Kirchhoff plate problem on surfaces embedded in three dimensions, along with numerical examples. We also describe a post-processing technique for approximating the surface Hessian of a scalar function from discrete data. We show how this scheme is easily extended to give convergent approximations of the *full shape operator* of the underlying surface, even for piecewise linear triangulations. Several numerical examples are given on non-trivial surfaces to illustrate the method. We then show how the surface HHJ finite element can also be used in computing Willmore flow, which is a gradient flow for the bending energy. In particular, we present key identities for the derivation of the method and discuss its stability. Several numerical examples show the efficacy of the method.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    Finding equilibrium states of fluid membranes
    11th Floor Lecture Hall
    • Speaker
    • Maxim Olshanskiy, University of Houston
    • Session Chair
    • Axel Voigt, Institute of Scientific Computing - Technische Universitat Dresden
    Abstract
    We are interested in finding equilibrium configurations of inextensible elastic membranes exhibiting lateral fluidity. Differential equations governing the mechanical equilibrium are derived using a continuum description of the membrane motions given by the surface Navier--Stokes equations with bending forces. Equilibrium conditions that are found appear to be independent of lateral viscosity and relate tension, pressure and tangential velocity of the fluid. These conditions yield that only surfaces with Killing vector fields, such as axisymmetric shapes, can support non-zero stationary flow of mass. We derive a shape equation that extends a classical Helfrich model with area constraint to membranes of non-negligible mass. We introduce a simple numerical method to compute solutions of this highly non-linear equation. The numerical method is then applied to find a diverse family of equilibrium configurations.
  • 11:30 am - 12:15 pm EDT
    Liquid Crystal Variational Problems
    11th Floor Lecture Hall
    • Speaker
    • Ricardo Nochetto, University of Maryland
    • Session Chair
    • Axel Voigt, Institute of Scientific Computing - Technische Universitat Dresden
    Abstract
    We discuss modeling, numerical analysis and computation of liquid crystal networks (LCNs). These materials couple a nematic liquid crystal with a rubbery material. When actuated with heat or light, the interaction of the liquid crystal with the rubber creates complex shapes. Thin bodies of LCNs are natural candidates for soft robotics applications. We start from the classical 3D trace energy formula and derive a reduced 2D membrane energy as the formal asymptotic limit of vanishing thickness and characterize the zero energy deformations. We design a sound numerical method and prove its Gamma convergence despite the strong nonlinearity and lack of convexity properties of the membrane energy. We present computations showing the geometric effects that arise from liquid crystal defects as well as computations of nonisometric origami within and beyond the theory. This work is joint with L. Bouck and S. Yang.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    A finite element scheme for the Q-tensor model of liquid crystals subjected to an electric field
    11th Floor Lecture Hall
    • Virtual Speaker
    • Franziska Weber, Carnegie Mellon University
    • Session Chair
    • Axel Voigt, Institute of Scientific Computing - Technische Universitat Dresden
    Abstract
    Liquid crystal is an intermediate state of matter between the liquid and the solid phase, where the elongated molecules of the material are in partial alignment. Due to this, materials exhibiting a liquid crystal phase have unique physical properties that are used in various real-life applications, such as monitors (LCDs), smart glasses, navigation systems, shampoos, and others. Various mathematical models are available to describe their dynamics, one commonly used one is the Q-tensor model by Landau and de Gennes, in which the alignment of the liquid crystal molecules and its variation over time are described through systems of nonlinear PDEs. In this talk, I will describe this model for the case where the liquid crystal molecules are subject to an electric field and present an energy-stable numerical discretization for it. Furthermore, within a particular range of material parameters, the convergence of the scheme can be shown to a weak solution of the system of PDEs. This is a joint work with Max Hirsch (UC Berkeley).
  • 3:30 - 4:00 pm EDT
    "Pi Day" Coffee Break
    Coffee Break - 11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    Numerical Approximation of the Stochastic Allen-Cahn Equation
    11th Floor Lecture Hall
    • Speaker
    • Noel Walkington, Carnegie Mellon University
    • Session Chair
    • Axel Voigt, Institute of Scientific Computing - Technische Universitat Dresden
    Abstract
    Convergence theory for numerical approximations of the stochastic Allen-Cahn equation will be reviewed. This talk will illustrate how structural properties of the partial differential operator(s) and probabilistic methods can be combined to establish stability and convergence of numerical schemes to approximate martingale solutions of the Allen-Cahn equation. This is joint work with M. Ondrejat (Prague, CZ) and A. Prohl (Tuebingen, DE).
Friday, March 15, 2024
  • 9:00 - 9:45 am EDT
    PDE: spectra, geometry and spectral geometry
    11th Floor Lecture Hall
    • Speaker
    • Nilima Nigam, Simon Fraser University
    • Session Chair
    • Noel Walkington, Carnegie Mellon University
    Abstract
    The spectra of elliptic operators are intricately connected to the geometrical properties of the spatial domains on which the operators are defined. Numerical computations are invaluable in studying this interplay, and high-accuracy discretizations are needed. This is particularly true of the Steklov problems. In this talk we'll present strategies for computing Steklov-Laplace and Steklov-Helmholtz spectra based on integral operators, and their efficacy in solving questions on the impact of geometry on spectral asymptotics. If time permits, we'll also present work in progress on a (modification of) the Steklov-Maxwell problem.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    Numerical analysis of an evolving bulk–surface model of tumour growth
    11th Floor Lecture Hall
    • Speaker
    • Balázs Kovács, University of Paderborn
    • Session Chair
    • Noel Walkington, Carnegie Mellon University
    Abstract
    In this talk we will discuss an evolving bulk--surface finite element method for a model of tissue growth, which is a modification of the model of Eyles, King and Styles (2019). The model couples a Poisson equation on the domain with a forced mean curvature flow of the free boundary, with nontrivial bulk-surface coupling in both the velocity law of the evolving surface and the boundary condition of the Poisson equation. The numerical method discretizes evolution equations for the mean curvature and the outer normal and it uses a harmonic extension of the surface velocity into the bulk. The discretization admits a convergence analysis in the case of continuous finite elements of polynomial degree at least two. The stability of the discretized bulk-surface coupling is a major concern. The error analysis combines stability estimates and consistency estimates to yield optimal-order H^1-norm error bounds for the computed tissue pressure and for the surface position, velocity, normal vector and mean curvature. We will present some numerical experiments illustrating and complementing our theoretical results. The talk is based on joint work with D. Edelmann and Ch. Lubich (Tuebingen).
  • 11:30 am - 12:15 pm EDT
    Phase Field Models and Continuous Data Assimilation
    11th Floor Lecture Hall
    • Speaker
    • Amanda Diegel, Mississippi State University
    • Session Chair
    • Noel Walkington, Carnegie Mellon University
    Abstract
    Phase field models have become popular tools that help capture important features of a variety of physical processes. In this talk, we will briefly discuss two popular models for phase separation: the Allen-Cahn equation and the Chan-Hilliard equation. We will then discuss finite element methods that incorporate continuous data assimilation in order to achieve long time accuracy and stability for arbitrarily inaccurate initial conditions provided enough data measurements are incorporated into the simulation. We will demonstrate the effectiveness of our methods via several numerical experiments.
  • 12:30 - 2:30 pm EDT
    Lunch/Free Time
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, March 18, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, March 19, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 11:00 am - 12:00 pm EDT
    WaveHoltz: Parallel and Scalable Solution of the Helmholtz Equation via Wave Equation Iteration
    11th Floor Lecture Hall
    • Daniel Appelö, Virginia Tech
    Abstract
    We introduce the WaveHoltz iteration, for solving the Helmholtz equation. The method is inspired by recent work on exact controllability (EC) methods and as in EC methods we make use of time domain methods for wave equations to design frequency domain Helmholtz solvers, but unlike EC methods we do not require adjoint solves. We show that the WaveHoltz iteration is symmetric and positive definite (compared to the indefinite Helmholtz equation). We present numerical examples, using various discretization techniques, that show that our method can be used to solve problems with rather high wave numbers.
  • 12:00 - 12:30 pm EDT
    Hybridizable discontinuous Galerkin method
    Post Doc/Graduate Student Seminar - 11th Floor Conference Room
    • Yukun Yue, University of Wisconsin, Madison
  • 12:30 - 1:00 pm EDT
    PDE constrained optimization
    Post Doc/Graduate Student Seminar - 11th Floor Conference Room
    • Sijing Liu, Brown University
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, March 20, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 11:00 am - 12:00 pm EDT
    Babuska's paradox in linear and nonlinear bending theories
    11th Floor Lecture Hall
    • Soeren Bartels, University of Freiburg
    Abstract
    The plate bending or Babuska paradox refers to the failure of convergence when a linear bending problem with simple support boundary conditions is approximated using polygonal domain approximations. We provide an explanation based on a variational viewpoint and identify sufficient conditions that avoid the paradox and which show that boundary conditions have to be suitably modified. We show that the paradox also matters in nonlinear thin-sheet folding problems and devise approximations that correctly converge to the original problem.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, March 21, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, March 22, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, March 25, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, March 26, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 11:00 am - 12:00 pm EDT
    The proximal Galerkin method
    11th Floor Lecture Hall
    • Thomas Surowiec, SIMULA
  • 12:00 - 1:00 pm EDT
    Long short-term memory (LSTM) neural networks
    Post Doc/Graduate Student Seminar - 11th Floor Conference Room
    • John Carter, Rensselaer Polytechnic Institute
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, March 27, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, March 28, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, March 29, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 9:30 - 10:30 am EDT
    Hiring
    Professional Development - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, April 1, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, April 2, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 11:00 am - 12:00 pm EDT
    A meeting of Stokes, Brinkman, and Darcy in polytopal multiscale hybrid methods
    11th Floor Lecture Hall
    • Sônia Gomes, Universidade Estadual de Campinas
  • 12:00 - 1:00 pm EDT
    Randomized SVD
    Post Doc/Graduate Student Seminar - 11th Floor Conference Room
    • Christopher Wang, Cornell University
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, April 3, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 11:00 am - 12:00 pm EDT
    Nonoverlapping Spectral Additive Schwarz Methods
    11th Floor Lecture Hall
    • Marcus Sarkis, Worcester Polytechnic Institute
    Abstract
    Nonoverlapping Spectral Additive Schwarz Methods-NOSAS is a family of adaptive Schwarz preconditioners designed originally for solving elliptic problems with highly heterogeneous coefficients with prescribed rate of convergence. And later extended to the Helmholtz problem. In this talk I will give a short introduction on Domain Decomposition methods as a preconditioner and then discuss NOSAS. This is a joint work with Yu Yi and Maksymilian Dryja.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, April 4, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, April 5, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 9:30 - 10:30 am EDT
    Papers
    Professional Development - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, April 8, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 2:00 - 3:00 pm EDT
    Eclipse Coffee Break
    Coffee Break - 11th Floor Collaborative Space
Tuesday, April 9, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 11:00 am - 12:00 pm EDT
    Adaptive algorithms for stochastic finite element methods
    11th Floor Lecture Hall
    • Alex Bespalov, University of Birmingham
    Abstract
    We will discuss a posteriori error estimation techniques and adaptive algorithms for two popular, albeit conceptually different, FEM-based solution strategies for partial differential equations with uncertain or parameter-dependent inputs: one strategy is projection-based (stochastic Galerkin FEM) and the other is sampling-based (stochastic collocation FEM).
  • 12:00 - 1:00 pm EDT
    Multigrid Part 1
    Post Doc/Graduate Student Seminar - 11th Floor Conference Room
    • Sijing Liu, Brown University
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, April 10, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 9:30 - 10:30 am EDT
    Grants
    Professional Development - 11th Floor Lecture Hall
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, April 11, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 11:00 am - 12:00 pm EDT
    Numerical schemes for the Cahn-Hilliard equation
    11th Floor Lecture Hall
    • Giordano Tierra Chica, University of North Texas
    Abstract
    The study of interfacial dynamics has become a key component to understand the behavior of a great variety of systems, in scientific, engineering and industrial applications. A very effective approach for representing interface problems is the diffuse interface/phase field approach, which describes the interfaces by layers of small thickness and whose structure is determined by a balance of molecular forces, in such a way that the tendencies for mixing and de-mixing compete through a non-local mixing energy. This approach uses a phase-field function that takes distinct values in the pure phases (for instance 0 in one phase and 1 in the other one) and varies smoothly in the interfacial regions. In particular, the Cahn- Hilliard equation was originally introduced to model the thermodynamic forces driving phase separation, arriving to a system with a gradient flow structure, that is, when there are no external forces applied to the system, the total free energy of the mixture is not increasing in time. In the first part of the presentation I will talk about the Cahn-Hilliard model and the main ideas behind the derivation of numerical schemes, showing the main advantages and disadvantages of each approach. The key point is to try to preserve the properties of the original model while the numerical schemes are efficient in time. On the second part I will present two new numerical schemes to approximate the Cahn-Hilliard equation with degenerate mobility. I will show that both schemes are energy stable and boundedness preserving, in the sense that the amount of the solution being outside of the interval [0, 1] goes to zero in terms of a truncation parameter. Finally, I will discuss how the ideas considered for designing numerical schemes to approximate phase-fields models can be extended to other energy based applications, like liquid crystals or mixture of fluids.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, April 12, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 9:00 - 10:00 am EDT
    Finite element discretization of nonlocal problems
    Tutorial - 11th Floor Lecture Hall
    • Christian Glusa, Sandia National Lab
  • 10:00 - 10:30 am EDT
    Break
    Coffee Break
  • 10:30 am - 12:30 pm EDT
    Hands-on session for PyNucleus
    Tutorial - 11th Floor Lecture Hall
    • Christian Glusa, Sandia National Lab
    Abstract
    Instructions for installing and running "PyNucleus" can be found here: https://sandialabs.github.io/PyNucleus/installation.html In order to make sure that learners can run the code locally on their machine on the day of the tutorial, I would recommend to follow the instructions for using the container image beforehand.
  • 12:30 - 1:30 pm EDT
    Lunch/Free Time
  • 1:30 - 2:30 pm EDT
    Overview of peridynamics and its meshfree discretization
    Tutorial - 11th Floor Lecture Hall
    • Pablo Seleson, Oak Ridge National Laboratory (ORNL)
    Abstract
    Peridynamics is a popular nonlocal formulation of continuum mechanics which has been shown to be highly effective for fracture modeling. A meshfree discretization is commonly used in peridynamics for engineering computations due to its implementation simplicity and its ability to easily handle large deformation and material separation. The PDMATLAB2D code is a meshfree peridynamics implementation in MATLAB suitable for simulation of two-dimensional fracture problems. PDMATLAB2D provides an entry-level peridynamics computational tool for both research and education. This short course will provide an overview of peridynamics and its meshfree discretization followed by a description of the PDMATLAB2D code and a hands-on session with illustrative examples.
    Materials: PDMATLAB2D code: The code can be downloaded from GitHub: https://github.com/ORNL/PDMATLAB2D/ PDMATLAB2D paper: The following paper describes the code: P. Seleson, M. Pasetto, Y. John, J. Trageser, S. T. Reeve. PDMATLAB2D: A Peridynamics MATLAB Two-dimensional Code. J Peridyn Nonlocal Model (2024). https://doi.org/10.1007/s42102-023-00104-w
    The paper can be accessed by clicking here.
    Instructions:
    Although it is not required, it is recommended that short-course attendees read the paper and download and run the code before the short course. The code can be directly downloaded by selecting the green Code button on the main repository page. Examples can be run (from the top-level directory) in MATLAB using either of the following commands: PDMATLAB2D('WavePropagation') PDMATLAB2D('CrackBranching')
  • 2:30 - 3:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:00 - 5:00 pm EDT
    Description of PDMATLAB2D and hands-on session
    Tutorial - 11th Floor Lecture Hall
    • Pablo Seleson, Oak Ridge National Laboratory (ORNL)
    Abstract
    PDMATLAB2D: A Meshfree Peridynamics MATLAB Code for 2D Fracture Computations
    Peridynamics is a popular nonlocal formulation of continuum mechanics which has been shown to be highly effective for fracture modeling. A meshfree discretization is commonly used in peridynamics for engineering computations due to its implementation simplicity and its ability to easily handle large deformation and material separation. The PDMATLAB2D code is a meshfree peridynamics implementation in MATLAB suitable for simulation of two-dimensional fracture problems. PDMATLAB2D provides an entry-level peridynamics computational tool for both research and education. This short course will provide an overview of peridynamics and its meshfree discretization followed by a description of the PDMATLAB2D code and a hands-on session with illustrative examples.
    Materials: PDMATLAB2D code: The code can be downloaded from GitHub: https://github.com/ORNL/PDMATLAB2D/ PDMATLAB2D paper: The following paper describes the code: P. Seleson, M. Pasetto, Y. John, J. Trageser, S. T. Reeve. PDMATLAB2D: A Peridynamics MATLAB Two-dimensional Code. J Peridyn Nonlocal Model (2024). https://doi.org/10.1007/s42102-023-00104-w <br< The paper can be accessed by clicking here. Instructions: Although it is not required, it is recommended that short-course attendees read the paper and download and run the code before the short course. The code can be directly downloaded by selecting the green Code button on the main repository page. Examples can be run (from the top-level directory) in MATLAB using either of the following commands: PDMATLAB2D('WavePropagation') PDMATLAB2D('CrackBranching')
Monday, April 15, 2024
  • 8:30 - 8:50 am EDT
    Check In
    11th Floor Collaborative Space
  • 8:50 - 9:00 am EDT
    Welcome
    11th Floor Lecture Hall
  • 9:00 - 10:20 am EDT
    An invitation to nonlocal models
    Tutorial - 11th Floor Lecture Hall
    • Speaker
    • Xiaochuan Tian, University of California-San Diego
    • Session Chair
    • Abner Salgado, University of Tennessee
    Abstract
    There has been a growing interest in studying nonlocal models as more general and sometimes more realistic alternatives to conventional PDE models. In this tutorial, we will introduce nonlocal models. In particular, we will focus on the nonlocal models with a finite range of nonlocal interactions, which connect the classical PDEs, nonlocal discrete models, and fractional differential equations. This talk will cover nonlocal modeling, nonlocal vector calculus, and numerical analysis for the nonlocal models.
  • 10:30 - 11:00 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 11:00 am - 12:20 pm EDT
    Tutorial on fractional calculus
    Tutorial - 11th Floor Lecture Hall
    • Speaker
    • Abner Salgado, University of Tennessee
    • Session Chair
    • Pablo Seleson, Oak Ridge National Laboratory (ORNL)
    Abstract
    We will discuss several approaches to extend the notion of a derivative to a fractional order, their meaning, limitations, and possible applications. For some of these, we will study the existence, uniqueness, and regularity of solutions to initial boundary value problems with these operators, and their implications for numerical approximations
  • 12:30 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 3:20 pm EDT
    Tutorial on peridynamics
    Tutorial - 11th Floor Lecture Hall
    • Speaker
    • Pablo Seleson, Oak Ridge National Laboratory (ORNL)
    • Session Chair
    • Xiaochuan Tian, University of California-San Diego
    Abstract
    Peridynamics is a powerful nonlocal reformulation of classical continuum mechanics, suitable for material failure and damage simulation, which has become very popular in recent years. In contrast to classical constitutive relations that employ spatial differential operators, peridynamic models use spatial integral operators which do not require spatial differentiability assumptions of displacement fields. This enables a natural representation of material discontinuities such as cracks. Peridynamic models possess length scales, making them also suitable for multiscale modeling. This tutorial will provide an overview of peridynamics, including some of its mathematical, computational, and modeling aspects.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    Analytical and applied aspects for nonlocal curvature
    11th Floor Lecture Hall
    • Speaker
    • Petronela Radu, University of Nebraska, Lincoln
    • Session Chair
    • Xiaochuan Tian, University of California-San Diego
    Abstract
    Curvature is a fundamental concept in physics and it plays a crucial role in various areas such as: classical mechanics, general relativity, optics, and fluid dynamics. In particular, the curvature of surfaces can affect the mechanical, electrical, and optical properties of materials, so curvature effects need to be taken into account when designing and analyzing new materials. The recently introduced concept of nonlocal curvatures provide a frameworks for measuring the “bend” of a surface under little or no smoothness assumptions, while connecting to classical curvature as the horizon of interaction converges to zero. In this talk I will focus on two distinct problems: of constant nonlocal curvature and of ordered curvature and show how they relate to their classical counterparts.
  • 5:00 - 6:30 pm EDT
    Reception
    11th Floor Collaborative Space
Tuesday, April 16, 2024
  • 9:00 - 9:45 am EDT
    Quasi-linear fractional operators in Lipschitz domains: regularity and approximation
    11th Floor Lecture Hall
    • Speaker
    • Ricardo Nochetto, University of Maryland
    • Session Chair
    • Abner Salgado, University of Tennessee
    Abstract
    Fractional diffusion in bounded domains is notorious for the lack of boundary regularity of solutions regardless of the smoothness of domain boundary. We explore this matter for the homogeneous Dirichlet problem for fractional-order quasi-linear operators with variable coefficients in Lipschitz domains and any dimensions; this includes fractional p-Laplacians and operators with finite horizon. We prove lift theorems in Besov norms which are consistent with the boundary behavior of solutions in smooth domains. The proof exploits the underlying variational structure and uses a new and flexible local translation operator. We further apply these regularity estimates to derive novel error estimates for finite element approximations of fractional p-Laplacians and present several simulations that reveal the boundary behavior of solutions.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    The role of fractional diffusion in the optimal recovery of partial differential equations without boundary conditions
    11th Floor Lecture Hall
    • Speaker
    • Andrea Bonito, Texas A&M University
    • Session Chair
    • Abner Salgado, University of Tennessee
    Abstract
    The problem of learning an unknown function from given data, i.e., construct an approximation to the function that predicts its values away from the data is ubiquitous in modern science. There are numerous settings for this learning problem depending on what additional information is provided about the unknown function, how the accuracy is measured, what is known about the data and data sites, and whether the data observations are polluted by noise. We consider the specific case where the learning problem consists of determining the solution to a second order elliptic partial differential equation (PDE) without information on its boundary condition. The lack of sufficient information necessary to uniquely determine the targeted function is alleviated by given finitely many linear noiseless measurements. The recovery performance is measured in energy norm and for the recovery problem to be tractable, we assume that the function to be recovered belongs to a compact subset of the energy space. The latter is referred to as the model class assumption. Among all functions satisfying the measurements, the PDE, and the model class assumption, the proposed algorithm constructs an approximation of the representative with minimal norm. For each measurement, this requires the approximation of a fractional diffusion problem on the boundary of the computational domain. We present and discuss the performances of the Dunford-Taylor method employed for the space discretization. In addition, we show how the resulting recovery algorithm is near-optimal and asymptotically optimal in the limit of the vanishing space discretization error.
  • 11:30 am - 12:15 pm EDT
    Peridynamic differential operator for optimum 3D Point Cloud Data manipulation
    11th Floor Lecture Hall
    • Speaker
    • Erdogan Madenci, University of Arizona
    • Session Chair
    • Abner Salgado, University of Tennessee
    Abstract
    Point cloud data (PCD) represents 3D spatial information as a set of points in a 3D coordinate system, typically obtained from various sensors such as LiDAR (Light Detection And Ranging). 3D PCD generated by LiDAR is accurate and precise; however, it can be massive, requiring significant storage and computational resources for extracting meaningful information from PCD sets. Also, the sparse and irregular nature of the data renders the compression process a challenging task. Furthermore, the raw data inevitably may contain outliers or noise in real-world situations. Majority of the current methods for compression of 3D PCD usually use sampling approaches to select points from the original point clouds for conducting local feature learning. A major drawback of the existing methods is that they are highly data-specific, challenge-specific, or approach-specific. This study presents an approach for optimized manipulation of 3D PCD to achieve high fidelity reconstruction of 3D LiDAR data by employing the Peridynamic Differential Operator (PDDO). It is a single mathematical framework for optimum and accurate data compression and decompression in the presence of irregularities and scatter in a multi-dimensional space. The capability of this approach is demonstrated by considering a 3D LiDAR PCD for adaptive data compression and recovery.
  • 12:30 - 2:30 pm EDT
    Poster Session Lunch
    Poster Session - 10th Floor Collaborative Space
  • 2:30 - 3:15 pm EDT
    Coupled local and nonlocal models
    11th Floor Lecture Hall
    • Speaker
    • Juan Pablo Borthagaray, Universidad de la República, Uruguay
    • Session Chair
    • Abner Salgado, University of Tennessee
    Abstract
    We consider theoretical and computational aspects of models coupling local and nonlocal operators with variable diffusivity. We discuss the well-posedness and strong formulation of such problems, as well as the regularity of weak solutions. We also focus on the approximation of solutions by a conforming finite element method.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 4:45 pm EDT
    Scalable methods for nonlocal models
    11th Floor Lecture Hall
    • Speaker
    • Christian Glusa, Sandia National Lab
    • Session Chair
    • Abner Salgado, University of Tennessee
    Abstract
    The naive discretization of nonlocal operators leads to matrices with significant density, as compared to classical PDEs. This makes the efficient solution of nonlocal models a challenging task. In this presentation, we will discuss ongoing research into efficient hierarchical matrix assembly and geometric and algebraic multigrid preconditioners that are suitable for nonlocal models.
Wednesday, April 17, 2024
  • 9:00 - 9:45 am EDT
    Some challenges in the numerical simulation of nonlocal models with a finite range of interactions.
    11th Floor Lecture Hall
    • Speaker
    • Qiang Du, Columbia University
    • Session Chair
    • Xiaochuan Tian, University of California-San Diego
    Abstract
    Nonlocal models associated with a finite horizon parameter that characterizes the effective range of nonlocal interactions have demonstrated potential as effective alternatives to local partial differential equations (PDEs) in various applications, such as the study of fracture and damage using peridynamics, and traffic flow of autonomous vehicles using nonlocal traffic models. However, to enhance the predictive capabilities and broaden the applicability of such models, new challenges arise in their numerical simulations. We provide illustrative examples, encompassing both theoretical analysis and practical implementation. These include choices regarding discretization methods, approximations of interaction neighborhoods, treatment of interfaces and boundaries, learning of nonlocal interactions from data, a priori and a posteriori error estimations, adaptive computation techniques, and the development of fast and scalable solvers.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    The role of boundary constraints in simulating biological systems with nonlocal dispersal.
    11th Floor Lecture Hall
    • Speaker
    • Gabriela Jaramillo, University of Houston
    • Session Chair
    • Xiaochuan Tian, University of California-San Diego
    Abstract
    Population and vegetation models often use nonlocal forms of dispersal to describe the spread of individuals and plants. When these long-range effects are modeled by spatially extended convolution kernels, the mathematical analysis of solutions can be simplified by posing the relevant equations on unbounded domains. However, in order to numerically validate these results, these same equations then need to be restricted to bounded sets. Thus, it becomes important to understand what effects, if any, do the different boundary constraints have on the solution. To address this question we present a quadrature method valid for convolution kernels with finite second moments. This scheme is designed to approximate at the same time the convolution operator together with the prescribed nonlocal boundary constraints, which can be Dirichlet, Neumann, or what we refer to as free boundary constraints. We then apply this scheme to study pulse solutions of an abstract 1-d nonlocal Gray-Scott model as a case study. We consider convolution kernels with exponential and with algebraic decay. We find that, surprisingly, boundary effects can be more prominent when using exponentially decaying kernels.
  • 11:30 am - 12:15 pm EDT
    Pointwise-in-time a-priori and a-posteriori error control for time-fractional subdiffusion equations
    11th Floor Lecture Hall
    • Speaker
    • Natalia Kopteva, University of Limerick
    • Session Chair
    • Xiaochuan Tian, University of California-San Diego
    Abstract
    Over the past decade, there has been a growing interest in evolution equations of parabolic type that involve fractional-order derivatives in time of order in (0, 1). Such equations, also called subdiffusion equations, arise in various applications in engineering, physics, biology and finance. Hence, it is quite important to develop efficient and reliable computational tools for their numerical solution. For such problems, I will present a simple and general numerical-stability analysis using barrier functions, which yields sharp pointwise-in-time error bounds. Furthermore, pointwise-in-time a posteriori error bounds will be given, which lead to an adaptive time stepping algorithm with a local time step criterion.
  • 12:25 - 12:30 pm EDT
    Group Photo (Immediately After Talk)
    11th Floor Lecture Hall
  • 12:30 - 12:40 pm EDT
    Semester Program group photos
    Group Photo (Immediately After Talk) - 11th Floor Lecture Hall
  • 12:40 - 2:30 pm EDT
    Lunch/Free Time
  • 2:30 - 3:15 pm EDT
    Learning Nonlocal Operators for Material Modeling
    11th Floor Lecture Hall
    • Speaker
    • Yue Yu, Lehigh University
    • Session Chair
    • Xiaochuan Tian, University of California-San Diego
    Abstract
    During the last 20 years there has been a lot of progress in applying neural networks (NNs) to many machine learning tasks. However, their employment in scientific machine learning with the purpose of learning complex responses of physical systems from experimental measurements has been explored much less. Unlike classical machine learning tasks, such as computer vision and natural language processing where a large amount of unstructured data are available, physics-based machine learning tasks often feature scarce and structured measurements. In this talk, we will consider learning of heterogeneous material responses as an exemplar problem to investigate automated physical model discovery from experimental data. In particular, we propose to parameterize the mapping between excitation and corresponding system responses in the form of nonlocal neural operators, and infer the neural network parameters from experimental measurements. As such, the model is built as mappings between infinite-dimensional function spaces, and the learnt network parameters are resolution-agnostic: measurements with different resolutions can be integrated to train the same model. Moreover, the nonlocal operator architecture also allows the incorporation of fundamental mathematical and physics knowledge, which further improves the learning efficacy and robustness from scarce measurements. To demonstrate the applicability of our nonlocal operator learning framework, three typical scenarios in physics-based machine learning will be discussed: (1) learning of a material-specific constitutive law, (2) learning of an efficient PDE solution operator, and (3) development of a foundation constitutive law across multiple materials. As an application, we learn material models directly from digital image correlation (DIC) displacement tracking measurements on a porcine tricuspid valve leaflet tissue, and we will show that the learnt model substantially outperforms conventional constitutive models.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 5:00 pm EDT
    TOPIC: Where is "nonlocal" going?
    Panel Discussion - 11th Floor Lecture Hall
    • Moderator
    • Abner Salgado, University of Tennessee
    • Panelists
    • Florin Bobaru, UNIVERSITY OF NEBRASKA–LINCOLN
    • Qiang Du, Columbia University
    • Ricardo Nochetto, University of Maryland
Thursday, April 18, 2024
  • 9:00 - 9:45 am EDT
    A Feynman-Kac probabilistic approach for the computation of nonlocal transport
    11th Floor Lecture Hall
    • Speaker
    • Diego del Castillo-Negrete, ORNL
    • Session Chair
    • Juan Pablo Borthagaray, Universidad de la República, Uruguay
    Abstract
    A novel method to compute nonlocal transport is presented [1]. The models of interest are Fokker-Planck type equations in which local (e.g., diffusive) transport is represented by differential operators and nonlocal transport by integrodifferential operators (e.g., non-diffusive turbulent transport closures and fractional diffusion). Computational approaches for these problems can be roughly classified as deterministic methods (e.g., finite-difference) and stochastic methods (e.g., Monte-Carlo). Although extensively used, continuum deterministic methods face stability and scalability challenges specially in the case of nonlocal operators that result in dense (non-sparse) matrices. On the other hand, particle-based stochastic methods face poor convergence due to statistical sampling. Here we present an alternative approach based on the Feynman-Kac theory that establishes a link between the Fokker-Planck equation and the stochastic differential equation of the underlying stochastic process. In local transport, the SDE are driven by Brownian motion and in nonlocal transport, depending on the nonlocal kernel, by compound Poisson processes or alpha-stable processes. The proposed method reduces the computation to the evaluation of expectations (bypassing the need of sampling stochastic trajectories) and it is unconditionally stable and parallelizable. We present applications to exit time and initial value problems for local and nonlocal transport in fluid dynamics and plasma physics. [1] M. Yang, G. Zhang, D. del-Castillo-Negrete, and Y.Cao, “A probabilistic scheme for semilinear nonlocal diffusion equations with volume constrains.” SIAM Journal of Numerical Analysis 61, (6), 2718-2743 (2023).
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    The "flexibility" of the peridynamic horizon
    11th Floor Lecture Hall
    • Speaker
    • Florin Bobaru, UNIVERSITY OF NEBRASKA–LINCOLN
    • Session Chair
    • Juan Pablo Borthagaray, Universidad de la República, Uruguay
    Abstract
    In any nonlocal model of a physical phenomenon, one has to decide the extent of the nonlocality. In peridynamics (PD), nonlocality is defined by the “horizon region”, with its radius (when taken as a circular disk in 2D, or a sphere in 3D), the PD horizon size. In certain cases, particular material length scales are prominent and measurable. For example, the size of inclusions in a matrix leads to specific wave scattering effects. Material properties (elastic moduli, fracture toughness) and loading conditions also lead to identifiable length scales. One can then select the PD horizon (and the PD kernel) of a homogenized model of heterogeneous material to be in the same range as that particular length scale. A more complex scenario is when several length scales are present in a material, and not all of them are easily quantifiable, or when they combine in some complex fashion. I will discuss the options for selecting a “proper” size for the peridynamic horizon for a particular model. While for generic isotropic and homogeneous elastic materials subject to homogeneous deformations one can select an arbitrary horizon size (the response will be the same, in the bulk), when deformations are not homogeneous, as they happen to be near holes or notches, the horizon has to be selected in relation to the dimensions of these geometrical details. When a material has such a multitude of holes that we have to “rename” it as a porous material, homogenization can be used to allow using a much larger horizon size than the minute size of the pores. In fracture problems, regular homogenization for such materials may not be able to capture the observed failure modes, and an “intermediately-homogenized” PD model may be needed to be able to predict fracture and damage in such material systems at a lower cost than models that represent the detailed, pore-level microstructure. Distinguishing experiments that create thresholds in terms of crack behavior can also be used to decide on the appropriate size of the peridynamic horizon. An example from thermally-induced fracture in glass will be shown. I will conclude with progress in speeding up peridynamic computations that use the fast convolution-based method (FCBM, see PeriFast codes on GitHub).
  • 11:30 am - 12:15 pm EDT
    Efficient approximation of nonlocal phase-field models in the context of solidification
    11th Floor Lecture Hall
    • Speaker
    • Olena Burkovska, Oak Ridge National Laboratory
    • Session Chair
    • Andrea Bonito, Texas A&M University
    Abstract
    Phase-field modeling is widely used in material science to describe dynamics of substances with multiple phases, and it is indispensable to model solidification of materials in additive manufacturing. The interface between two substances, which is usually sharp, is replaced by a diffuse interface phase-field model that avoids an explicit tracking of the moving boundary. Resolving very thin interfaces in existing phase-field models requires very fine meshes or adding more structural complexity to the model in order to accurately capture the sharp interface. As a remedy, we propose a novel non-isothermal model with coupled local-nonlocal dynamics. This provably allows to provide sharper interfaces in the solution up to the mesh resolution and can help to alleviate the limitations of resolving thin diffuse interfaces. Additionally, we design spatial and temporal discretization schemes that allow for efficient practical realizations of those models. We propose first and second-order time-stepping schemes, which guarantee energy stability in the isothermal case, and combine them with the finite element or spectral approximations in space. A particular structure of the model and nonlocal kernel allows for the characterization of the solution in terms of a projection formula. This provides an efficient way to evaluate the solution, and in some cases avoids solving a coupled nonlinear and nonlocal system.
  • 12:30 - 2:30 pm EDT
    Networking Lunch
    Lunch/Free Time - 11th Floor Collaborative Space
  • 2:30 - 3:15 pm EDT
    On overcoming challenges in capturing corrosion dynamics using a nonlocally defined degradation field
    11th Floor Lecture Hall
    • Speaker
    • Cynthia Flores, California State University, Channel Islands
    • Session Chair
    • Andrea Bonito, Texas A&M University
    Abstract
    In this talk, we introduce corrosion degradation fields defined nonlocally. Emphasizing the challenge of defining boundary conditions for the nonlocal generation of current density maps, we explore the application of a simplified nonlocal Finite Element (FE) fractional-Laplacian solver for modeling corrosion degradation, with a particular focus on aerospace environments. We discuss the involvement of undergraduate researchers and the interdisciplinary validation of theoretical models through experimental data obtained using a Scanning Reference Electrode Technique (SRET) apparatus, with a specific focus on the aerospace context and the consideration of Microbiologically Induced Corrosion (MIC).
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:00 - 5:00 pm EDT
    TOPIC: Funding opportunities
    Panel Discussion - 11th Floor Lecture Hall
    • Moderator
    • Yue Yu, Lehigh University
    • Panelists
    • Yuliya Gorb, NSF
    • Michael Parks, Oak Ridge National Laboratory
    • Ludmil Zikatanov, The Pennsylvania State University
Friday, April 19, 2024
  • 9:00 - 9:45 am EDT
    Computation and applications of the variable-order fractional Laplacian
    11th Floor Lecture Hall
    • Speaker
    • Yanzhi Zhang, Missouri University of Sciences and Technology
    • Session Chair
    • Xiaochuan Tian, University of California-San Diego
    Abstract
    The variable-order fractional Laplacian plays an important role in the study of heterogeneous systems. However, current numerical methods for computing the variable-order fractional Laplacian still remain limited. Compared to its constant-order counterpart, the combination of nonlocality and heterogeneity in variable-order fractional Laplacian introduces significant storage and computational challenges. Consequently, many numerical methods developed for the constant-order fractional Laplacian become ineffective for computing the variable-order cases. In this talk, we introduce two numerical methods for the the variable-order Laplacian as well as their fast implementation. Some application of the variable-order fractional Laplacian in diffusion and wave propagation in heterogeneous media will also be discussed.
  • 10:00 - 10:30 am EDT
    Coffee Break
    11th Floor Collaborative Space
  • 10:30 - 11:15 am EDT
    Analysis of Crack Patterns and Multi-term Time-fractional Dynamics using CNNs and Fractional Physics-informed DeepONet
    11th Floor Lecture Hall
    • Speaker
    • Guang Lin, Purdue University
    • Session Chair
    • Christian Glusa, Sandia National Lab
    Abstract
    In this talk, we first introduce convolutional neural networks designed to predict and analyze damage patterns on a disk resulting from molecular dynamic collision simulations. We propose the use of neural network approximations to complement peridynamic simulations by providing quick estimates which maintain much of the accuracy of the full simulations while reducing simulation times by a factor of 1500. We propose two distinct convolutional neural networks: one trained to perform the forward problem of predicting the damage pattern on a disk provided the location of a colliding object’s impact, and another trained to solve the inverse problem of identifying the collision location, angle, velocity, and size given the resulting damage pattern. Second, we introduce a Physics-informed DeepONet model to solve the multi-term time-fractional mixed diffusion equations. Deep Operator networks such as DeepONet can approximate nonlinear operators between infinite dimensional Banach spaces. PINN-DeepONet employs deep neural operator networks with the PDEs explicitly encoded into the Neural Networks using automatic differentiation to impose the underlying physical laws via soft penalty constraints during model training. Here we extend PINN-DeepONet to fractional physics-informed DeepONets to solve multi-term time-fractional mixed diffusion-wave equations. We demonstrate that the proposed method can not only yield a significant improvement in predictive accuracy but also reduce the need for large training data sets.
  • 11:30 am - 12:15 pm EDT
    Analysing the temporal accuracy of a hierarchy of coarse-grained SDE models
    11th Floor Lecture Hall
    • Speaker
    • Xingjie Li, University of North Carolina at Charlotte
    • Session Chair
    • Abner Salgado, University of Tennessee
    Abstract
    Coarse-graining or model reduction of dynamical systems is a modelling tool used to extend the time-scale of simulations in a range of fields. When applied in molecular dynamics with moderate time-scale separations, standard coarse-graining approaches seek to approximate the potential of mean force, and use this to drive an effective model. Meanwhile, there is no free lunch: fewer degrees of freedom necessarily means lower accuracy of the resulting model. Here, I will discuss work with Dr Thomas Hudson from the University of Warwick, UK, in which we derived a hierarchy of models to coarse-grain simple systems and analysed the resulting models. It is shown that while the standard recipe for model reduction accurately captures equilibrium statistics, it is possible to derive an easy-to-implement Markovian effective model to better capture dynamical statistics such as the mean-squared displacement. Our results focus particularly on the temporal accuracy of coarse-grained models. Both analytical and numerical evidence for the efficacy of the new approach is provided.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, April 22, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, April 23, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 12:00 - 1:00 pm EDT
    Multigrid Part 2
    Post Doc/Graduate Student Seminar - 11th Floor Conference Room
    • Casey Cavanaugh, Louisiana State University
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, April 24, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, April 25, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 11:00 am - 12:00 pm EDT
    A quasi-incompressible Chan-Hilliard-Darcy model for two-phase flows in porous media
    11th Floor Lecture Hall
    • Daozhi Han, State University of New York at Buffalo
    Abstract
    Two-phase flows in porous media is known as the Muskat problem. The Muskat problem can be ill-posed. In this talk we introduce a quasi-incompressible Cahn-Hilliard-Darcy model as a relaxation of the Muskat problem. We show global existence of weak solution to the model. We then present a high order accurate bound-preserving and unconditionally stable numerical method for solving the equations.
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, April 26, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, April 29, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, April 30, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 12:00 - 1:00 pm EDT
    The unfitted finite element method
    Post Doc/Graduate Student Seminar - 11th Floor Conference Room
    • Henry von Wahl, Friedrich Schiller University Jena
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, May 1, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 12:00 - 1:00 pm EDT
    End of Semester Lunch
    Working Lunch - 11th Floor Collaborative Space
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, May 2, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Friday, May 3, 2024
Numerical PDEs: Analysis, Algorithms, and Data Challenges
  • 3:30 - 4:00 pm EDT
    Coffee Break
    11th Floor Collaborative Space

All event times are listed in ICERM local time in Providence, RI (Eastern Daylight Time / UTC-4).

All event times are listed in .

Application Information

This program is at capacity, and ICERM is no longer accepting applications.

Your Visit to ICERM

ICERM Facilities
ICERM is located on the 10th & 11th floors of 121 South Main Street in Providence, Rhode Island. ICERM's business hours are 8:30am - 5:00pm during this event. See our facilities page for more info about ICERM and Brown's available facilities.
Traveling to ICERM
ICERM is located at Brown University in Providence, Rhode Island. Providence's T.F. Green Airport (15 minutes south) and Boston's Logan Airport (1 hour north) are the closest airports. Providence is also on Amtrak's Northeast Corridor. In-depth directions and transportation information are available on our travel page.
Lodging/Housing
Visiting ICERM for longer than a week-long workshop? ICERM staff works with participants to locate accommodations that fit their needs. Since short-term furnished housing is in very high demand, take advantage of the housing options ICERM may recommend. Contact housing@icerm.brown.edu for more details.
Childcare/Schools
Those traveling with family who are interested in information about childcare and/or schools should contact housing@icerm.brown.edu.
Technology Resources
Wireless internet access and wireless printing is available for all ICERM visitors. Eduroam is available for members of participating institutions. Thin clients in all offices and common areas provide open access to a web browser, SSH terminal, and printing capability. See our Technology Resources page for setup instructions and to learn about all available technology.
Accessibility
To request special services, accommodations, or assistance for this event, please contact accessibility@icerm.brown.edu as far in advance of the event as possible. Thank you.
Discrimination and Harassment Policy
ICERM is committed to creating a safe, professional, and welcoming environment that benefits from the diversity and experiences of all its participants. Brown University's "Code of Conduct", "Discrimination and Workplace Harassment Policy", "Sexual and Gender-based Misconduct Policy", and "Title IX Policy" apply to all ICERM participants and staff. Participants with concerns or requests for assistance on a discrimination or harassment issue should contact the ICERM Director or Assistant Director Jenna Sousa; they are the responsible employees at ICERM under this policy.
Fundamental Research
ICERM research programs aim to promote Fundamental Research and mathematical sciences education. If you are engaged in sensitive or proprietary work, please be aware that ICERM programs often have participants from countries and entities subject to United States export control restrictions. Any discoveries of economically significant intellectual property supported by ICERM funding should be disclosed.
Exploring Providence
Providence's world-renowned culinary scene provides ample options for lunch and dinner. Neighborhoods near campus, including College Hill Historic District, have many local attractions. Check out the map on our Explore Providence page to see what's near ICERM.

Visa Information

Contact visa@icerm.brown.edu for assistance.

Need a US Visa?
J-1 visa requested via ICERM staff
Eligible to be reimbursed
B-1 or Visa Waiver Business (WB) –if you already have either visa – contact ICERM staff for a visa specific invitation letter.
Ineligible to be reimbursed
B-2 or Visa Waiver Tourist (WT)
Already in the US?

F-1 and J-1 not sponsored by ICERM: obtain a letter approving reimbursement from the International Office of your home institution PRIOR to travel.

H-1B holders do not need letter of approval.

All other visas: alert ICERM staff immediately about your situation.

ICERM does not reimburse visa fees. This chart is to inform visitors whether the visa they enter the US on allows them to receive reimbursement for the items outlined in their invitation letter.

Financial Support

This section is for general purposes only and does not indicate that all attendees receive funding. Please refer to your personalized invitation to review your offer.

ORCID iD
As this program is funded by the National Science Foundation (NSF), ICERM is required to collect your ORCID iD if you are receiving funding to attend this program. Be sure to add your ORCID iD to your Cube profile as soon as possible to avoid delaying your reimbursement.
Acceptable Costs
  • 1 roundtrip between your home institute and ICERM
  • Flights on U.S. or E.U. airlines – economy class to either Providence airport (PVD) or Boston airport (BOS)
  • Ground Transportation to and from airports and ICERM.
Unacceptable Costs
  • Flights on non-U.S. or non-E.U. airlines
  • Flights on U.K. airlines
  • Seats in economy plus, business class, or first class
  • Change ticket fees of any kind
  • Multi-use bus passes
  • Meals or incidentals
Advance Approval Required
  • Personal car travel to ICERM from outside New England
  • Multiple-destination plane ticket; does not include layovers to reach ICERM
  • Arriving or departing from ICERM more than a day before or day after the program
  • Multiple trips to ICERM
  • Rental car to/from ICERM
  • Flights on a Swiss, Japanese, or Australian airlines
  • Arriving or departing from airport other than PVD/BOS or home institution's local airport
  • 2 one-way plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
Travel Maximum Contributions
  • New England: $350
  • Other contiguous US: $850
  • Asia & Oceania: $2,000
  • All other locations: $1,500
  • Note these rates were updated in Spring 2023 and superseded any prior invitation rates. Any invitations without travel support will still not receive travel support.
Reimbursement Requests

Request Reimbursement with Cube

Refer to the back of your ID badge for more information. Checklists are available at the front desk and in the Reimbursement section of Cube.

Reimbursement Tips
  • Scanned original receipts are required for all expenses
  • Airfare receipt must show full itinerary and payment
  • ICERM does not offer per diem or meal reimbursement
  • Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via pdf of Google Maps result
  • Keep all documentation until you receive your reimbursement!
Reimbursement Timing

6 - 8 weeks after all documentation is sent to ICERM. All reimbursement requests are reviewed by numerous central offices at Brown who may request additional documentation.

Reimbursement Deadline

Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. Submissions after thirty days will incur applicable taxes. No submissions are accepted more than six months after the program end.

Associated Semester Workshops

Numerical Analysis of Multiphysics Problems
Image for "Numerical Analysis of Multiphysics Problems"
PDEs and Geometry: Numerical Aspects
Image for "PDEs and Geometry: Numerical Aspects"