Organizing Committee
Abstract

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.

Image for "Numerical Methods for Large-Scale Nonlinear Problems and Their Applications"
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.

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, August 31, 2015
TimeEventLocationMaterials
8:30 - 8:45am EDTRegistration: Numerical Methods for Large-Scale Nonlinear Problems and Their Applications11th Floor Collaborative Space 
8:30 - 8:45am EDTRegistration: Numerical Methods for Large-Scale Nonlinear Problems and Their Applications11th Floor Collaborative Space 
8:45 - 9:00am EDTWelcome and Introductory Remarks - ICERM Director, Organizers11th Floor Lecture Hall 
9:00 - 10:00am EDTComments on Anderson Acceleration, Mixing and Extrapolation - Donald Anderson, Harvard University11th Floor Lecture Hall
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:00am EDTAnderson acceleration for time-dependent problems - Rob Haelterman, Royal Military Academy (School)11th Floor Lecture Hall
11:15 - 11:45am EDTAcceleration, inexact Newton, and Nonlinear Krylov subspace methods - Yousef Saad, University of Minnesota11th Floor Lecture Hall
12:00 - 12:30pm EDTComparing Anderson Acceleration to Newton-based Solvers on Multiphysics Systems - Roger Pawlowski, Sandia National Laboratories11th Floor Lecture Hall 
12:30 - 2:00pm EDTBreak for lunch  
2:00 - 2:30pm EDTImplicit integration methods for dislocation dynamics - David Gardner, Lawrence Livermore National Laboratory11th Floor Lecture Hall
2:45 - 3:15pm EDTAnderson Acceleration- Convergence Theory and Numerical Experience - Tim Kelley, NCSU11th Floor Lecture Hall
3:15 - 3:45pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:45 - 4:15pm EDTA Hybrid Deterministic-Monte Carlo Thermal Radiative Transfer Solver with High-Order, Low-Order Method - HyeongKae Park, Los Alamos National Laboratory11th Floor Lecture Hall
4:15 - 5:00pm EDTDiscussion: How has Anderson acceleration impacted the nonlinear solvers community? - Moderators: Tim Kelley, Homer Walker 11th Floor Lecture Hall 
5:00 - 6:30pm EDTWelcome Reception11th Floor Collaborative Space 
Tuesday, September 1, 2015
TimeEventLocationMaterials
9:00 - 9:30am EDTPreconditioner Updates for Solving Sequences of Linear Systems arising in inexact methods for optimization. - Stefania Bellavia, University of Florence11th Floor Lecture Hall
9:45 - 10:15am EDTNonlinear FETI-DP and BDDC Domain Decomposition Methods - Axel Klawonn, University of Cologne Mathematical Institute11th Floor Lecture Hall
10:15 - 10:45am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:45 - 11:15am EDTLeveraging time integration to increase efficiency and robustness of nonlinear implicit solvers - Daniel Reynolds, Southern Methodist University11th Floor Lecture Hall
11:30 - 12:00pm EDTNo equations, no variables- data, and the computational modeling of complex systems. - Yannis Kevrekidis, Princeton University11th Floor Lecture Hall
12:00 - 2:00pm EDTBreak for lunch  
2:00 - 2:30pm EDTAn Integrated Study of Modeling, Discretization and Preconditioning for Magnetohydrodynamics - Jinchao Xu, Pennsylvania State University11th Floor Lecture Hall
2:45 - 3:15pm EDTAMGe Coarse Spaces with Approximation Properties - Panayot Vassilevski, Lawrence Livermore National Laboratory11th Floor Lecture Hall
3:15 - 3:45pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:45 - 4:15pm EDTModeling Physical Processes from Hydraulic Fracturing to Long-term Production - Mary Wheeler, University of Texas at Austin11th Floor Lecture Hall
4:15 - 6:00pm EDTPoster Session11th Floor Lecture Hall and Collaborative Space 
Wednesday, September 2, 2015
TimeEventLocationMaterials
9:00 - 9:30am EDTGeneralized Derivatives- Automatic Evaluation and Implications for Algorithms - Paul Barton, Massachusetts Institute of Technology11th Floor Lecture Hall
9:45 - 10:15am EDTOn piecewise smooth optimization and algebraic inclusion solving - Andreas Griewank, Humboldt University of Berlin11th Floor Lecture Hall
10:15 - 10:45am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:45 - 11:15am EDTNon-Intrusive Algorithms for Measure-Theoretic Propagation of Uncertainties- Errors, Opportunities, and Challenges - Troy Butler, University of Colorado Denver11th Floor Lecture Hall
11:30 - 12:00pm EDTAdjoint-Based a Posteriori Error Estimation and Uncertainty Quantification for Transient Nonlinear Problems with Discontinuous Solutions - Timothy Wildey, Sandia National Laboratories11th Floor Lecture Hall
12:00 - 12:05pm EDTWorkshop Group Photo  
12:05 - 2:00pm EDTBreak for lunch  
2:00 - 2:30pm EDTNonlinear Schwarz Preconditioning - David Keyes, King Abdullah University of Science & Technology11th Floor Lecture Hall
2:45 - 3:15pm EDTMultiphysics Simulations- Challenges and Opportunities - Carol Woodward, Lawrence Livermore National Laboratory11th Floor Lecture Hall
3:15 - 3:45pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:45 - 4:15pm EDTScalable Implicit - IMEX Resistive MHD with Stabilized Finite Element Methods and Fully-coupled Solution Methods - John Shadid, Sandia National Laboratories11th Floor Lecture Hall
4:15 - 5:00pm EDTDiscussion: How can the nonlinear solvers community impact multiphysics simulations? - Moderators: John Shadid, Carol Woodward 11th Floor Lecture Hall 
Thursday, September 3, 2015
TimeEventLocationMaterials
9:00 - 9:30am EDTWhy Exascale Computing Will Be Slightly Less Disruptive Than the Comet that Killed the Dinosaurs - Jeffrey Hittinger, Lawrence Livermore National Laboratory11th Floor Lecture Hall
9:45 - 10:15am EDTConsiderations on efficient implementation of Anderson acceleration on parallel architectures - John Loffeld, Lawrence Livermore National Laboratory11th Floor Lecture Hall
10:15 - 10:45am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:45 - 12:00pm EDTTopic- How should the nonlinear-solvers community prepare for future HPC architectures - Panel- Jeffrey Hittinger, David Keyes, Matthew Knepley, Roger Pawlowski11th Floor Lecture Hall
12:00 - 2:00pm EDTBreak for lunch  
2:00 - 2:30pm EDTEfforts to implement and optimize nonlinear solvers within DOE’s Accelerated Climate Model for Energy (ACME) - Katherine Evans, Oak Ridge National Laboratory11th Floor Lecture Hall
2:45 - 3:15pm EDTNonlinear Preconditioning and Applications - Xiao-Chuan Cai, University of Colorado11th Floor Lecture Hall
3:15 - 3:45pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:45 - 4:15pm EDTA fully implicit, exactly conserving algorithm for multidimensional particle-in-cell kinetic simulations - Luis Chacon, Los Alamos National Laboratory11th Floor Lecture Hall
4:30 - 5:00pm EDTAnderson acceleration for Tiamat - Alexander Toth, North Carolina State University11th Floor Lecture Hall
Friday, September 4, 2015
TimeEventLocationMaterials
9:00 - 9:30am EDTUncertainty Quantification of Multiphysics Systems Through Nonlinear Elimination and Measure Transformation - Eric Phipps, Sandia National Laboratories11th Floor Lecture Hall
9:45 - 10:15am EDTAccelerating the EM algorithm for mixture density estimation - Homer Walker, WPI and ICERM11th Floor Lecture Hall
10:15 - 10:45am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:45 - 11:15am EDTComposing Nonlinear Solvers - Matthew Knepley, University of Chicago11th Floor Lecture Hall
11:30 - 12:15pm EDTDiscussion: What are the next big challenges for the nonlinear solvers community? - Moderators: Tim Kelley, Homer Walker, Carol Woodward11th Floor Lecture Hall 

Lecture Videos

Composing Nonlinear Solvers

Matt Knepley
Rice University
September 4, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides

Accelerating the EM algorithm for mixture density estimation

Homer Walker
Worcester Polytechnic Institute
September 4, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides

Uncertainty Quantification of Multiphysics Systems Through Nonlinear Elimination and Measure Transformation

Eric Phipps
Sandia National Laboratory
September 4, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides

Anderson acceleration for Tiamat

Alex Toth
North Carolina State University
September 3, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides

A fully implicit, exactly conserving algorithm for multidimensional particle-in-cell kinetic simulations

Luis Chacon
LANL
September 3, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides

Efforts to implement and optimize nonlinear solvers within DOE's Accelerated Climate Model for Energy (ACME)

Kate Evans
ORNL
September 3, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract

Considerations on efficient implementation of Anderson acceleration on parallel architectures

Jon Loffeld
Lawrence Livermore National Laboratory
September 3, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides

Why Exascale Computing Will Be Slightly Less Disruptive Than the Comet that Killed the Dinosaurs

Jeff Hittinger
LLNL
September 3, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides

Nonlinear Schwarz Preconditioning

David Keyes
King Abdullah University of Science and Technology
September 2, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides

Adjoint-Based a Posteriori Error Estimation and Uncertainty Quantification for Transient Nonlinear Problems with Discontinuous Solutions

Tim Wildey
Sandia National Laboratory
September 2, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract

Non-Intrusive Algorithms for Measure-Theoretic Propagation of Uncertainties- Errors, Opportunities, and Challenges

Troy Butler
University of Colorado - Denver
September 2, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides

On piecewise smooth optimization and algebraic inclusion solving

Andreas Griewank
Institut für Mathematik
September 2, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides

Generalized Derivatives- Automatic Evaluation and Implications for Algorithms

Paul Barton
MIT
September 2, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides

AMGe Coarse Spaces with Approximation Properties

Panayot Vassilevski
LLNL
September 1, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract

Leveraging time integration to increase efficiency and robustness of nonlinear implicit solvers

Daniel Reynolds
Southern Methodist University
September 1, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides

Preconditioner Updates for Solving Sequences of Linear Systems arising in inexact methods for optimization

Stefania Bellavia
University of Florence
September 1, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides

Anderson Acceleration: Convergence Theory and Numerical Experience

Tim Kelley
NCSU
August 31, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract

Implicit integration methods for dislocation dynamics

David Gardner
Lawrence Livermore National Laboratory
August 31, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides

Acceleration, inexact Newton, and Nonlinear Krylov subspace methods

Yousef Saad
University of Minnesota
August 31, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides

Anderson acceleration for time-dependent problems

Rob Haelterman
Royal Military Academy
August 31, 2015
Numerical Methods for Large-Scale Nonlinear Problems and Their Applications
Play     Abstract     Slides