Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
(August 31 - September 4, 2015)

Picture
Simulation of an unstable 3D incompressible planar jet at Reynolds
number 108 showing streamwise Kelvin-Helmholtz instability and
secondary cross-stream instability. Image courtesy of John Shadid,
Sandia National Labs, to appear in joint work with L. Chacon,
E. C. Cyr, A. A. Oberai, R. P. Pawlowski, T. Smith, D. Sondak,
R. S. Tuminaro, and P. D. Weber.

Description

Over the last 20 years or so, Newton-Krylov methods have developed to maturity, allowing effective fully-coupled treatment of a broad range of large-scale nonlinear problems. This development has set the stage for addressing more difficult problems with more challenging features. Additionally, applications for which state-of-the-art Newton-Krylov approaches are inapplicable have recently exposed several basic research questions. At the same time, there remain many problem-specific methods and legacy codes that are still useful and can be regarded as a resource for further development.

This workshop will include mathematicians and computer scientists who work on algorithm design, implementation, and analysis, together with disciplinary scientists and engineers who use the algorithms in applications and have a working knowledge of their capabilities, weaknesses, and limitations. The major foci of the workshop will be acceleration methods, in particular Anderson acceleration; methods for nonlinear problems that have significant stochastic aspects; methods for nonsmooth problems; and various techniques for improving robustness, such as nonlinear preconditioning.

Organizing Committee

(* = Speaker)
  • James Adler
    (Tufts University)
  • Shahriar Afkhami
    (New Jersey Institute of Technology)
  • Steven Allmaras
    (MIT)
  • Hengbin An
    (Worcester Polytechnic Institute)
  • Donald Anderson*
    (Harvard University)
  • Paul Barton *
    (Massachusetts Institute of Technology)
  • Stefania Bellavia *
    (Università di Firenze)
  • Troy Butler*
    (University of Colorado Denver)
  • Xiao-Chuan Cai *
    (University of Colorado)
  • Carlos Cardoso Borges
    (Courant Institute of Mathematical Sciences - New Y)
  • Marco Ceze
    (NASA Ames Research Center)
  • Luis Chacon*
    (Los Alamos National Laboratory)
  • Minseok Choi
    (Brown University)
  • Geoffrey Dillon
    (Virginia Tech)
  • Jon Erwin
    (University of Tennessee)
  • Katherine Evans *
    (Oak Ridge National Laboratory)
  • Marshall Galbraith
    (MIT)
  • David Gardner *
    (Lawrence Livermore National Laboratory)
  • Ryan Glasby
    (University of Tennessee)
  • Christian Glusa
    (Brown University)
  • Andreas Griewank*
    (Humboldt-Universität)
  • Rob Haelterman*
    (Royal Military Academy (School))
  • Jeff Hittinger *
    (Lawrence Livermore National Laboratory)
  • Xiaozhe Hu
    (Tufts University)
  • Tim Kelley *
    (North Carolina State University)
  • Yannis Kevrekidis *
    (Princeton University)
  • David Keyes *
    (King Abdullah University of Science & Technology)
  • Abdul Qayyum Khaliq
    (Middle Tennessee State University)
  • Arkadz Kirshtein
    (Penn State)
  • Axel Klawonn*
    (University of Cologne Mathematical Institute)
  • Matt Knepley *
    (University of Chicago)
  • Andrew Knyazev
    (Mitsubishi Electric Research Laboratories)
  • ANTONY LIAKOPOULOS
    (UNIVERSITY OF THESSALY / BROWN UNIVERSITY)
  • Lulu Liu
    (King Abdullah University of Science and Technology)
  • Yicong Ma
    (Pennsylvania State University)
  • Vijay Mahadevan
    (Argonne National Laboratory)
  • Matthias Mayr
    (Technische Universität München)
  • Razvan Mezei
    (Lenoir-Rhyne University)
  • HyeongKae Park*
    (Los Alamos National Laboratory)
  • Kailash C. Patidar
    (University of the Western Cape)
  • Roger Pawlowski*
    (Sandia National Laboratories)
  • Eric Phipps*
    (Sandia National Laboratories)
  • Sara Pollock
    (Texas A&M University)
  • Viktor Reshniak
    (Middle Tennessee State University)
  • Daniel Reynolds *
    (Southern Methodist University)
  • Yousef Saad *
    (University of Minnesota)
  • Anju Saini
    (Indian Institute of Technology)
  • John Shadid *
    (Sandia National Laboratories)
  • Ramjee Sharma
    (University of North Georgia)
  • Bedrich Sousedik
    (University of Maryland, Baltimore County)
  • Alex Toth*
    (North Carolina State University)
  • Benjamin Uekermann
    (Technische Universitaet Muenchen)
  • Panayot Vassilevski *
    (Lawrence Livermore National Laboratory)
  • Homer Walker *
    (Institute for Computational and Experimental Research in Mathematics (ICERM))
  • Mary Wheeler *
    (University of Texas at Austin)
  • Tim Wildey*
    (Sandia National Laboratories)
  • Carol Woodward *
    (Lawrence Livermore National Laboratory)
  • Shuonan Wu
    (Pennsylvania State University)
  • Yuanzhe Xi
    (University of Minnesota)
  • Jinchao Xu *
    (Pennsylvania State University)
  • Hongquan Zhang
    (Pennsylvania State University)
  • Lei Zhang
    (Shanghai Jiao Tong University)
  • Zhongqiang Zhang
    (Brown University)
Monday August 31, 2015
Time Description Speaker Location Abstracts Slides
8:30 - 8:45Registration: Numerical Methods for Large-Scale Nonlinear Problems and Their Applications11th Floor Collaborative Space
8:30 - 8:45Registration: Numerical Methods for Large-Scale Nonlinear Problems and Their Applications11th Floor Collaborative Space
8:45 - 9:00Welcome and Introductory RemarksICERM Director, Organizers11th Floor Lecture Hall
9:00 - 10:00Comments on Anderson Acceleration, Mixing and ExtrapolationDonald Anderson, Harvard University11th Floor Lecture Hall
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10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space
10:30 - 11:00Anderson acceleration for time-dependent problemsRob Haelterman, Royal Military Academy (School)11th Floor Lecture Hall
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11:15 - 11:45Acceleration, inexact Newton, and Nonlinear Krylov subspace methodsYousef Saad, University of Minnesota11th Floor Lecture Hall
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12:00 - 12:30Comparing Anderson Acceleration to Newton-based Solvers on Multiphysics SystemsRoger Pawlowski, Sandia National Laboratories11th Floor Lecture Hall
12:30 - 2:00Break for lunch
2:00 - 2:30Implicit integration methods for dislocation dynamicsDavid Gardner, Lawrence Livermore National Laboratory11th Floor Lecture Hall
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2:45 - 3:15Anderson Acceleration- Convergence Theory and Numerical ExperienceTim Kelley, NCSU11th Floor Lecture Hall
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3:15 - 3:45Coffee/Tea Break11th Floor Collaborative Space
3:45 - 4:15A Hybrid Deterministic-Monte Carlo Thermal Radiative Transfer Solver with High-Order, Low-Order MethodHyeongKae Park, Los Alamos National Laboratory11th Floor Lecture Hall
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4:15 - 5:00Discussion: How has Anderson acceleration impacted the nonlinear solvers community?Moderators: Tim Kelley, Homer Walker 11th Floor Lecture Hall
5:00 - 6:30Welcome Reception11th Floor Collaborative Space

Tuesday September 1, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 9:30Preconditioner Updates for Solving Sequences of Linear Systems arising in inexact methods for optimization.Stefania Bellavia, University of Florence11th Floor Lecture Hall
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9:45 - 10:15Nonlinear FETI-DP and BDDC Domain Decomposition MethodsAxel Klawonn, University of Cologne Mathematical Institute11th Floor Lecture Hall
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10:15 - 10:45Coffee/Tea Break11th Floor Collaborative Space
10:45 - 11:15Leveraging time integration to increase efficiency and robustness of nonlinear implicit solversDaniel Reynolds, Southern Methodist University11th Floor Lecture Hall
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11:30 - 12:00No equations, no variables- data, and the computational modeling of complex systems.Yannis Kevrekidis, Princeton University11th Floor Lecture Hall
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12:00 - 2:00Break for lunch
2:00 - 2:30An Integrated Study of Modeling, Discretization and Preconditioning for MagnetohydrodynamicsJinchao Xu, Pennsylvania State University11th Floor Lecture Hall
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2:45 - 3:15AMGe Coarse Spaces with Approximation PropertiesPanayot Vassilevski, Lawrence Livermore National Laboratory11th Floor Lecture Hall
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3:15 - 3:45Coffee/Tea Break11th Floor Collaborative Space
3:45 - 4:15Modeling Physical Processes from Hydraulic Fracturing to Long-term ProductionMary Wheeler, University of Texas at Austin11th Floor Lecture Hall
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4:15 - 6:00Poster Session11th Floor Lecture Hall and Collaborative Space

Wednesday September 2, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 9:30Generalized Derivatives- Automatic Evaluation and Implications for AlgorithmsPaul Barton, Massachusetts Institute of Technology11th Floor Lecture Hall
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9:45 - 10:15On piecewise smooth optimization and algebraic inclusion solvingAndreas Griewank, Humboldt University of Berlin11th Floor Lecture Hall
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10:15 - 10:45Coffee/Tea Break11th Floor Collaborative Space
10:45 - 11:15Non-Intrusive Algorithms for Measure-Theoretic Propagation of Uncertainties- Errors, Opportunities, and ChallengesTroy Butler, University of Colorado Denver11th Floor Lecture Hall
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11:30 - 12:00Adjoint-Based a Posteriori Error Estimation and Uncertainty Quantification for Transient Nonlinear Problems with Discontinuous SolutionsTimothy Wildey, Sandia National Laboratories11th Floor Lecture Hall
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12:00 - 12:05Workshop Group Photo
12:05 - 2:00Break for lunch
2:00 - 2:30Nonlinear Schwarz PreconditioningDavid Keyes, King Abdullah University of Science & Technology11th Floor Lecture Hall
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2:45 - 3:15Multiphysics Simulations- Challenges and OpportunitiesCarol Woodward, Lawrence Livermore National Laboratory11th Floor Lecture Hall
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3:15 - 3:45Coffee/Tea Break11th Floor Collaborative Space
3:45 - 4:15Scalable Implicit - IMEX Resistive MHD with Stabilized Finite Element Methods and Fully-coupled Solution MethodsJohn Shadid, Sandia National Laboratories11th Floor Lecture Hall
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4:15 - 5:00Discussion: How can the nonlinear solvers community impact multiphysics simulations?Moderators: John Shadid, Carol Woodward 11th Floor Lecture Hall

Thursday September 3, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 9:30Why Exascale Computing Will Be Slightly Less Disruptive Than the Comet that Killed the DinosaursJeffrey Hittinger, Lawrence Livermore National Laboratory11th Floor Lecture Hall
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9:45 - 10:15Considerations on efficient implementation of Anderson acceleration on parallel architecturesJohn Loffeld, Lawrence Livermore National Laboratory11th Floor Lecture Hall
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10:15 - 10:45Coffee/Tea Break11th Floor Collaborative Space
10:45 - 12:00Topic- How should the nonlinear-solvers community prepare for future HPC architecturesPanel- Jeffrey Hittinger, David Keyes, Matthew Knepley, Roger Pawlowski11th Floor Lecture Hall
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12:00 - 2:00Break for lunch
2:00 - 2:30Efforts to implement and optimize nonlinear solvers within DOE’s Accelerated Climate Model for Energy (ACME)Katherine Evans, Oak Ridge National Laboratory11th Floor Lecture Hall
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2:45 - 3:15Nonlinear Preconditioning and ApplicationsXiao-Chuan Cai, University of Colorado11th Floor Lecture Hall
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3:15 - 3:45Coffee/Tea Break11th Floor Collaborative Space
3:45 - 4:15A fully implicit, exactly conserving algorithm for multidimensional particle-in-cell kinetic simulationsLuis Chacon, Los Alamos National Laboratory11th Floor Lecture Hall
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4:30 - 5:00Anderson acceleration for TiamatAlexander Toth, North Carolina State University11th Floor Lecture Hall
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Friday September 4, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 9:30Uncertainty Quantification of Multiphysics Systems Through Nonlinear Elimination and Measure TransformationEric Phipps, Sandia National Laboratories11th Floor Lecture Hall
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9:45 - 10:15Accelerating the EM algorithm for mixture density estimationHomer Walker, WPI and ICERM11th Floor Lecture Hall
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10:15 - 10:45Coffee/Tea Break11th Floor Collaborative Space
10:45 - 11:15Composing Nonlinear SolversMatthew Knepley, University of Chicago11th Floor Lecture Hall
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11:30 - 12:15Discussion: What are the next big challenges for the nonlinear solvers community? Moderators: Tim Kelley, Homer Walker, Carol Woodward11th Floor Lecture Hall