Organizing Committee
Abstract

Most systems targeted by mathematical modeling in modern science and engineering are fundamentally multi-physical and multi-scale in nature. As such, they involve solving complex coupled, generally nonlinear, systems of partial differential equations (PDEs) built from subsystems of PDEs that mathematically model very different physical processes, often at very different scales.

Recent advances in high-performance computer hardware and advanced numerical algorithms have made it feasible to construct realistic mathematical models and to build corresponding numerical simulation software for these types of complex multi-physics/multi-scale problems. However, developing robust, efficient, and practical numerical algorithms for such simulation software that are capable of tackling these complex mathematical models is still extremely challenging in a number of fundamental ways. For example, we do not yet have robust methods that can handle strong coupling between different physics and/or scales, and we still do not have optimal linear solvers that can reliably and efficiently treat the discretized linearized systems.

This workshop will gather together experts in the core related fields in applied and computational mathematics to exchange ideas regarding the development of robust and efficient numerical schemes that preserve the key physics of these models, and to study the development of fast and efficient linear and nonlinear solvers that are scalable and optimal. This workshop will also target young researchers and members of under-represented groups to help launch their research in this area.

Confirmed Speakers & Participants

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

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, May 12, 2014
TimeEventLocationMaterials
8:30 - 8:55am EDTRegistration11th Floor Collaborative Space 
8:55 - 9:00am EDTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45am EDTStructure-preserving discretizations for computing multi-physics - Douglas N. Arnold, University of Minnesota11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTLocal Bounded Cochain Projections and the Bubble Transform - Ragnar Winther, University of Oslo11th Floor Lecture Hall
11:30 - 12:15pm EDTAdvances in the mathematical theory of the finite element immersed boundary method - Daniele Boffi, Universita di Pavia11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch and Free Time  
2:30 - 3:15pm EDTBasic Principles of Mixed Virtual Element Methods - Donatella Marini, Universita di Pavia11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTSolving multi-physics models with NGSolve - Joachim Schoberl, Technische Universitat Wien11th Floor Lecture Hall
5:00 - 6:00pm EDTWelcome Reception  
Tuesday, May 13, 2014
TimeEventLocationMaterials
9:00 - 9:45am EDTA Robust Methodology for the Numerical Solution of Fully Nonlinear Elliptic Problems - Roland Glowinski, University of Houston11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTA 3D hp Finite Element Code for Multiphysics Coupled Problems with Elements of All Shapes, Orientation Embedded Shape Functions, the Discontinuous Petrov Galerkin (DPG) Method and Other Stories - Leszek Demkowicz, The University of Texas at Austin11th Floor Lecture Hall
11:30 - 12:15pm EDTNumerical Methods of Quasicrystals - Pingwen Zhang, Peking University11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch and Free Time  
2:30 - 3:15pm EDTDiscretizing the Advection of Differential Forms - Ralf Hiptmair, ETH11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTOn the accuracy of finite element approximations to a class of interface problems - Johnny Guzman, Brown University11th Floor Lecture Hall
Wednesday, May 14, 2014
TimeEventLocationMaterials
9:00 - 9:45am EDTHydraulic Fracturing Modeling in Porous Media - Mary Wheeler, The University of Texas at Austin11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTRobust Discretization and Solution Strategies for Moving-Domain Fluid-Structure Interaction Problems - Yuri Bazilevs, University of California, San Diego11th Floor Lecture Hall
11:30 - 12:15pm EDTA priori and a posteriori analyses of DPG methods - Jay Gopalakrishnan, Portland State University11th Floor Lecture Hall
12:30 - 12:40pm EDTGroup Photo11th Floor Lecture Hall 
12:40 - 2:30pm EDTBreak for Lunch and Free Time  
2:30 - 3:15pm EDTQuantum Calculations in Solution for Large to Very Large Molecules- A New Linear Scaling QM:Continuum Approach - Yvon Maday, Sorbonne Universites and Brown University11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTCommuting projections on graphs - Ludmil Zikatanov, The Pennsylvania State University11th Floor Lecture Hall
7:00 - 8:30pm EDTPoster Session  
Thursday, May 15, 2014
TimeEventLocationMaterials
9:00 - 9:45am EDTBilayer Plates- Model Reduction, Analysis and Computation - Ricardo H. Nochetto, University of Maryland11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:15am EDTThe PML Method and Fast Solvers for the Helmholtz Equation in Unbounded Domain - Zhiming Chen, Chinese Academy of Sciences11th Floor Lecture Hall
11:30 - 12:15pm EDTNew Mixed Elements for Linear Elasticity Problems within the Hellinger-Reissner Variational Formulation - Jun Hu, Peking University11th Floor Lecture Hall
12:30 - 2:30pm EDTBreak for Lunch and Free Time  
2:30 - 3:15pm EDTMultiphysics Simulations- Challenges and Opportunities - Carol S. Woodward, Lawrence Livermore National Laboratory11th Floor Lecture Hall
3:15 - 3:15pm EDTPlease take a moment to complete the survey that was distributed by email.  
3:30 - 4:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm EDTDiscontinuous Galerkin Finite Element Method for Multiscale Problems - Chi-Wang Shu, Brown University11th Floor Lecture Hall
Friday, May 16, 2014
TimeEventLocationMaterials
8:30 - 9:15am EDTSpectral discretization and fast solvers for fractional PDEs - Mohsen Zayernouri, Brown University11th Floor Lecture Hall
9:30 - 10:15am EDTTwo stable discretizationsns for Non-Newtonian Flow Models - Young Ju Lee, Texas State University-San Marcos11th Floor Lecture Hall
10:30 - 10:45am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:45 - 11:30am EDTHP A+C: Systems for High Performance Analytics and High Performance Computing - Leopold Grinberg, IBM11th Floor Lecture Hall 
11:45 - 12:30pm EDTFast Solvers for Force-based Multi-physics Coupling Models - Mitchell Luskin, University of Minnesota11th Floor Lecture Hall
12:45 - 5:00pm EDTFree For Collaborations  

Lecture Videos

Discontinuous Galerkin Finite Element Method for Multiscale Problems

Chi-Wang Shu
Brown University
May 15, 2014
Robust Discretization and Fast Solvers for Computable Multi-Physics Models
Play     Abstract

New Mixed Elements for Linear Elasticity Problems within the Hellinger-Reissner Variational Formulation

Jun Hu
Beijing (Peking) University
May 15, 2014
Robust Discretization and Fast Solvers for Computable Multi-Physics Models
Play     Abstract

The PML Method and Fast Solvers for the Helmholtz Equation in Unbounded Domain

Zhiming Chen
Chinese Academy of Sciences, China
May 15, 2014
Robust Discretization and Fast Solvers for Computable Multi-Physics Models
Play     Abstract

A priori and a posteriori analyses of DPG methods

Jay Gopalakrishnan
Portland State University
May 14, 2014
Robust Discretization and Fast Solvers for Computable Multi-Physics Models
Play     Abstract     Slides

Discretizing the Advection of Differential Forms

Ralf Hiptmair
ETH
May 13, 2014
Robust Discretization and Fast Solvers for Computable Multi-Physics Models
Play     Abstract     Slides

Numerical Methods of Quasicrystals

Pingwen Zhang
Beijing (Peking) University
May 13, 2014
Robust Discretization and Fast Solvers for Computable Multi-Physics Models
Play     Abstract

A 3D hp Finite Element Code for Multiphysics Coupled Problems with Elements of All Shapes, Orientation Embedded Shape Functions, the Discontinuous Petrov Galerkin (DPG) Method and Other Stories

Leszek Demkowicz
University of Texas at Austin
May 13, 2014
Robust Discretization and Fast Solvers for Computable Multi-Physics Models
Play     Abstract     Slides

A Robust Methodology for the Numerical Solution of Fully Nonlinear Elliptic Problems

Roland Glowinski
University of Houston
May 13, 2014
Robust Discretization and Fast Solvers for Computable Multi-Physics Models
Play     Abstract

Basic Principles of Mixed Virtual Element Methods

Donatella Marini
Università di Pavia
May 12, 2014
Robust Discretization and Fast Solvers for Computable Multi-Physics Models
Play     Abstract

Local Bounded Cochain Projections and the Bubble Transform

Ragnar Winther
University of Oslo
May 12, 2014
Robust Discretization and Fast Solvers for Computable Multi-Physics Models
Play     Abstract

Structure-preserving discretizations for computing multi-physics

Douglas Arnold
University of Minnesota
May 12, 2014
Robust Discretization and Fast Solvers for Computable Multi-Physics Models
Play     Abstract