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.

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

Workshop Schedule

Monday, August 31, 2015
TimeEventLocationMaterials
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 Remarks - ICERM Director, Organizers11th Floor Lecture Hall 
9:00 - 10:00Comments on Anderson Acceleration, Mixing and Extrapolation - Donald Anderson, Harvard University11th Floor Lecture Hall
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:00Anderson acceleration for time-dependent problems - Rob Haelterman, Royal Military Academy (School)11th Floor Lecture Hall
11:15 - 11:45Acceleration, inexact Newton, and Nonlinear Krylov subspace methods - Yousef Saad, University of Minnesota11th Floor Lecture Hall
12:00 - 12:30Comparing Anderson Acceleration to Newton-based Solvers on Multiphysics Systems - Roger Pawlowski, Sandia National Laboratories11th Floor Lecture Hall 
12:30 - 2:00Break for lunch  
2:00 - 2:30Implicit integration methods for dislocation dynamics - David Gardner, Lawrence Livermore National Laboratory11th Floor Lecture Hall
2:45 - 3:15Anderson Acceleration- Convergence Theory and Numerical Experience - Tim Kelley, NCSU11th Floor Lecture Hall
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 Method - HyeongKae Park, Los Alamos National Laboratory11th Floor Lecture Hall
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
TimeEventLocationMaterials
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
9:45 - 10:15Nonlinear FETI-DP and BDDC Domain Decomposition Methods - Axel Klawonn, University of Cologne Mathematical Institute11th Floor Lecture Hall
10:15 - 10:45Coffee/Tea Break11th Floor Collaborative Space 
10:45 - 11:15Leveraging time integration to increase efficiency and robustness of nonlinear implicit solvers - Daniel Reynolds, Southern Methodist University11th Floor Lecture Hall
11:30 - 12:00No equations, no variables- data, and the computational modeling of complex systems. - Yannis Kevrekidis, Princeton University11th Floor Lecture Hall
12:00 - 2:00Break for lunch  
2:00 - 2:30An Integrated Study of Modeling, Discretization and Preconditioning for Magnetohydrodynamics - Jinchao Xu, Pennsylvania State University11th Floor Lecture Hall
2:45 - 3:15AMGe Coarse Spaces with Approximation Properties - Panayot Vassilevski, Lawrence Livermore National Laboratory11th Floor Lecture Hall
3:15 - 3:45Coffee/Tea Break11th Floor Collaborative Space 
3:45 - 4:15Modeling Physical Processes from Hydraulic Fracturing to Long-term Production - Mary Wheeler, University of Texas at Austin11th Floor Lecture Hall
4:15 - 6:00Poster Session11th Floor Lecture Hall and Collaborative Space 
Wednesday, September 2, 2015
TimeEventLocationMaterials
9:00 - 9:30Generalized Derivatives- Automatic Evaluation and Implications for Algorithms - Paul Barton, Massachusetts Institute of Technology11th Floor Lecture Hall
9:45 - 10:15On piecewise smooth optimization and algebraic inclusion solving - Andreas Griewank, Humboldt University of Berlin11th Floor Lecture Hall
10:15 - 10:45Coffee/Tea Break11th Floor Collaborative Space 
10:45 - 11:15Non-Intrusive Algorithms for Measure-Theoretic Propagation of Uncertainties- Errors, Opportunities, and Challenges - Troy Butler, University of Colorado Denver11th Floor Lecture Hall
11:30 - 12:00Adjoint-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 - 12:05Workshop Group Photo  
12:05 - 2:00Break for lunch  
2:00 - 2:30Nonlinear Schwarz Preconditioning - David Keyes, King Abdullah University of Science & Technology11th Floor Lecture Hall
2:45 - 3:15Multiphysics Simulations- Challenges and Opportunities - Carol Woodward, Lawrence Livermore National Laboratory11th Floor Lecture Hall
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 Methods - John Shadid, Sandia National Laboratories11th Floor Lecture Hall
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
TimeEventLocationMaterials
9:00 - 9:30Why 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 - 10:15Considerations on efficient implementation of Anderson acceleration on parallel architectures - John Loffeld, Lawrence Livermore National Laboratory11th Floor Lecture Hall
10:15 - 10:45Coffee/Tea Break11th Floor Collaborative Space 
10:45 - 12:00Topic- 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 - 2:00Break 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
2:45 - 3:15Nonlinear Preconditioning and Applications - Xiao-Chuan Cai, University of Colorado11th Floor Lecture Hall
3:15 - 3:45Coffee/Tea Break11th Floor Collaborative Space 
3:45 - 4:15A fully implicit, exactly conserving algorithm for multidimensional particle-in-cell kinetic simulations - Luis Chacon, Los Alamos National Laboratory11th Floor Lecture Hall
4:30 - 5:00Anderson acceleration for Tiamat - Alexander Toth, North Carolina State University11th Floor Lecture Hall
Friday, September 4, 2015
TimeEventLocationMaterials
9:00 - 9:30Uncertainty Quantification of Multiphysics Systems Through Nonlinear Elimination and Measure Transformation - Eric Phipps, Sandia National Laboratories11th Floor Lecture Hall
9:45 - 10:15Accelerating the EM algorithm for mixture density estimation - Homer Walker, WPI and ICERM11th Floor Lecture Hall
10:15 - 10:45Coffee/Tea Break11th Floor Collaborative Space 
10:45 - 11:15Composing Nonlinear Solvers - Matthew Knepley, University of Chicago11th Floor Lecture Hall
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 

Lecture Videos