Days: Wednesday, March 24th Thursday, March 25th Friday, March 26th Monday, March 29th Tuesday, March 30th Wednesday, March 31st Thursday, April 1st Friday, April 2nd
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Multigrid is one of the few optimal methods for solving systems of equations arising from the discretization of partial differential equations as well as a wide variety of related problems on graphs. In this tutorial we will introduce the key ingredients of the multigrid method (smoothing and coarse grid correction), explain their complementarity (they don't work well alone), and describe the most common cycling strategies. We will present the concepts and motivating analysis using a simple geometric approach to solving the linear system arising from the discretization of the diffusion equation on structured orthogonal grids. Then we will highlight the elements of the algorithm that have been advanced to provide robustness and flexibility for more general problems (e.g., operator dependent interpolation, galerkin coarse grid operators, and algebraic methods), noting that these topics will be covered in more detail in the subsequent tutorials. Finally, we'll touch on the popular and powerful use of multigrid as a preconditioner for Krylov methods such as the conjugate gradient method.
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The focus of this tutorial is on algebraic multigrid (AMG). The tutorial will start with the basic principles of algebraic multigrid methods, followed by introducing two general methods: CF based algebraic multigrid and aggregation based algebraic multigrid. An overview of these methods, including common algorithms for their construction will be covered. The goal is to identify the key components of AMG. Advanced algebraic methods such as compatible relaxation, adaptive AMG, and element based AMG will also be briefly covered. In addition, an overview of some of the supporting theory will be given.
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This tutorial will start with an introduction to parallel computing and cover the classical computer taxonomy, programming models, parallel performance metrics, and parallelizing PDE-based problems. The talk will then move on to parallel multigrid, including parallel algebraic multigrid and parallel multigrid software design. Finally, some current research topics will be touched on as well as a brief introduction to parallel time integration (multigrid in time).
View this program: with abstractssession overviewtalk overview
15:00 | Coarse Grid Selection using Simulated Annealing (abstract) PRESENTER: Tareq Uz Zaman |
15:25 | A Cut-Based Coarsening Algorithm for Smoothed Aggregation (abstract) |
15:50 | Algebraic multigrid preconditioner for statically condensed systems arising from lowest-order hybrid discretizations (abstract) PRESENTER: Pierre Matalon |
16:15 | A new semi-algebraic two-grid method for Oseen problems. (abstract) PRESENTER: Pierre-Loîc Bacq |
15:00 | Nonlinear FETI-DP Domain Decomposition Methods - Tailoring the Nonlinear Elimination Set (abstract) PRESENTER: Axel Klawonn |
15:25 | Globalization of Nonlinear FETI-DP Methods (abstract) PRESENTER: Stephan Köhler |
15:50 | Optimal order multigrid preconditioners for the distributed control of parabolic equations with coarsening in space and time (abstract) PRESENTER: Andrei Draganescu |
16:15 | Multigrid Methods for Elliptic Optimal Control Problems (abstract) PRESENTER: Sijing Liu |
17:20 | Layer-Parallel Training, Multilevel Network Initialization, and Local Learning (abstract) |
17:45 | Optimization-based Grid Coarsening Using Reinforcement Learning (abstract) PRESENTER: Ali Taghibakhshi |
18:10 | DiffGCN: Graph Convolutional Networks via Differential Operators and Algebraic Multigrid Pooling (abstract) PRESENTER: Eran Treister |
18:35 | A Supervised Learning Approach to Predicting Multigrid Convergence (abstract) PRESENTER: Nicolas Nytko |
17:20 | Porting an aggregation-based algebraic multigrid method on GPU (abstract) PRESENTER: Abdeselam El Haman Abdeselam |
17:45 | Algebraic multigrid using a stencil-CSR matrix format on GPUs (abstract) PRESENTER: Siham Boukhris |
18:10 | Communication-avoiding algebraic multigrid for high-performance computing (abstract) |
View this program: with abstractssession overviewtalk overview
15:00 | Symbol Based Multigrid Methods for Block Structured Matrices (abstract) PRESENTER: Isabella Furci |
15:25 | Multigrid Methods for Finite Element Approximations using a Block Symbol Approach (abstract) PRESENTER: Paola Ferrari |
15:50 | Complexity Analysis of Matrix-Free Multigrid with Surrogate Polynomials (abstract) |
16:15 | Anisotropic multigrid preconditioners for space-fractional diffusion equations (abstract) PRESENTER: Ken Trotti |
15:00 | A p-Multigrid Accelerated Hybrid Fourier-Chebyshev Collocation Method For Nonlinear Water Waves in Numerical Wave Tanks (abstract) PRESENTER: Anders Melander |
15:25 | A Generalized Multigrid Method for Contact problems in Unfitted Finite Element Methods} (abstract) PRESENTER: Hardik Kothari |
15:50 | Augmented Lagrangian preconditioner for anisothermal non-Newtonian flow (abstract) PRESENTER: Pablo Alexei Gazca Orozco |
16:15 | A local Fourier analysis of low order preconditioners for the Stokes equations (abstract) PRESENTER: Alexey Voronin |
17:20 | Learning optimal multigrid smoothers via neural networks (abstract) PRESENTER: Ru Huang |
17:45 | Combining machine learning and adaptive coarse spaces to design robust and efficient FETI-DP methods for elliptic problems in three dimensions (abstract) PRESENTER: Janine Weber |
18:10 | Globally Convergent Multilevel Training of Deep Residual Networks (abstract) PRESENTER: Alena Kopanicakova |
18:35 | Multiscale training for Physics-informed Neural Networks (abstract) PRESENTER: Ravi G. Patel |
17:20 | Multigrid injection operators for hybridized mixed and discontinuous Galerkin methods (abstract) PRESENTER: Andreas Rupp |
17:45 | Multilevel Preconditioning of the Reaction-Diffusion Problem (abstract) PRESENTER: Constantin Bacuta |
18:10 | p-refined Multilevel Quasi-Monte Carlo with Locally Nested Random Field Evaluation Points Applied to a Geotechnical Engineering Problem (abstract) PRESENTER: Philippe Blondeel |
18:35 | Effective material parameters from microstructures constructed using the planar Boolean model (abstract) PRESENTER: Matthias Brändel |
View this program: with abstractssession overviewtalk overview
15:00 | Multigrid Reduction in Time using Coarse-grid Agglomeration, approximate solves and Krylov acceleration (abstract) PRESENTER: Ryo Yoda |
15:25 | An overlapping and asynchronous Parareal-like algorithm (abstract) PRESENTER: Jens Hahne |
15:50 | Optimizing MGRIT and Parareal coarse-grid operators for linear advection (abstract) PRESENTER: Oliver Krzysik |
16:15 | Multi-step variant of the parareal algorithm: convergence analysis and numerics (abstract) PRESENTER: Katia Ait Ameur |
16:40 | Optimal Relaxation Weights for Multigrid Reduction In Time (MGRIT) (abstract) |
15:00 | Scalable minimum-residual multigrid solver for wave propagation (abstract) PRESENTER: Jacob Badger |
15:25 | Stand-alone multigrid for Helmholtz revisited: towards convergence using standard components (abstract) PRESENTER: Vandana Dwarka |
15:50 | Accelerating Krylov subspace actions of the matrix exponential by multigrid corrections (abstract) |
16:15 | Condensed Nonconforming Reformulations for Preconditioning Finite Element Discretization Problems (abstract) PRESENTER: Delyan Kalchev |
16:40 | CHRONOS: A GENERAL-PURPOSE AMG LINEAR SOLVER (abstract) PRESENTER: Giovanni Isotton |
17:45 | Monolithic multigrid methods for implicit Runge-Kutta discretizations of time-dependent PDEs (abstract) PRESENTER: Razan Abu-Labdeh |
18:10 | Robust Preconditioners for a Mimetic Finite-Difference Method for Maxwell's Equations (abstract) PRESENTER: Casey Cavanaugh |
18:35 | Multigrid-in-Channels Neural Network Architectures (abstract) PRESENTER: Moshe Eliasof |
View this program: with abstractssession overviewtalk overview
15:00 | Space-time block preconditioning for incompressible flow, and nonsymmetric AMG (abstract) PRESENTER: Ben Southworth |
15:25 | A geometrically-informed algebraic multigrid preconditioned iterative approach for solving high-order finite element systems (abstract) PRESENTER: Songzhe Xu |
15:50 | Matrix-Matrix based AMG interpolations and the GPU implementations (abstract) PRESENTER: Ruipeng Li |
16:15 | Aggregative Multiscale AMG: A robust interpolation approach for (plain) aggregative AMG based on ideas of Algebraic Multiscale (abstract) |
15:00 | Nonnegative Unimodal Matrix Factorization (abstract) PRESENTER: Andersen Man Shun Ang |
15:25 | New Two-level GPU-Accelerated Incomplete LU Preconditioners in hypre (abstract) PRESENTER: Tianshi Xu |
15:50 | A multigrid-inspired approach for the Augmented Block Cimmino Distributed solver (abstract) PRESENTER: Philippe Leleux |
16:15 | A New Block Preconditioner for Implicit Runge-Kutta Methods for Parabolic PDE Problems (abstract) PRESENTER: Md Masud Rana |
17:20 | Non-invasive multigrid for semi-structured grids (abstract) |
17:45 | Improving the fast diagonalization method for non-separable problems with subspace correction (abstract) PRESENTER: Pablo Brubeck |
18:10 | A Space-Time Multigrid Preconditioner for CFD (abstract) PRESENTER: Lea Miko Versbach |
18:35 | Optimization of two-level methods for DG discretizations of reaction-diffusion equations (abstract) PRESENTER: Jose Pablo Lucero Lorca |
17:20 | Additive Schwarz methods for serendipity elements (abstract) PRESENTER: Jorge Marchena Menendez |
17:45 | Scalable Chebyshev-Accelerated Schwarz Preconditioning for GPUs (abstract) PRESENTER: Malachi Phillips |
18:10 | Adaptive coarse spaces for Schwarz methods based on decompositions of the domain decomposition interface (abstract) PRESENTER: Jascha Knepper |
18:35 | Three-level Fast and Robust Overlapping Schwarz (FROSch) preconditioners (abstract) PRESENTER: Friederike Röver |
View this program: with abstractssession overviewtalk overview
15:00 | ILUT smoothers for p-multigrid methods in Isogeometric Analysis (abstract) PRESENTER: Cornelis Vuik |
15:25 | Non-overlapping block smoothers for the Stokes equations (abstract) PRESENTER: Lisa Claus |
15:50 | Smoothers Based on Nonoverlapping Domain Decomposition Methods for H(curl) problems (abstract) |
16:15 | Optimal polynomial smoothers for V-cycle multigrid (abstract) |
16:40 | Two-Stage Gauss-Seidel with Dropping for GMRES-AMG Solvers (abstract) PRESENTER: Stephen Thomas |
15:00 | FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica (abstract) PRESENTER: Alexander Heinlein |
15:25 | A Monolithic Algebraic Multigrid Approach for Coupled Multiphysics Problems using the MueLu Framework (abstract) PRESENTER: Peter Ohm |
15:50 | Monolithic Multigrid Methods for Mixed Formulations of the Biharmonic Problem (abstract) PRESENTER: Abdalaziz Hamdan |
16:15 | An algebraic multigrid method for mortar contact problems in saddle-point formulation (abstract) PRESENTER: Matthias Mayr |
17:20 | Multilevel methods with inexact solver on the coarsest level (abstract) PRESENTER: Petr Vacek |
17:45 | Local Fourier Analysis of P-Multigrid with LFAToolkit.jl (abstract) PRESENTER: Jeremy Thompson |
18:10 | Automated local Fourier analysis (aLFA) (abstract) PRESENTER: Karsten Kahl |
18:35 | Independence of placement for local Fourier analysis (abstract) |
17:45 | RCHOL: Randomized Cholesky Factorization for Solving SDD Linear Systems (abstract) PRESENTER: Chao Chen |
18:10 | A posteriori error estimates and its application in adaptive algebraic multigrid methods ($\alpha$AMG) for graph Laplacians (abstract) PRESENTER: Kaiyi Wu |
18:35 | A Multilevel Subgraph Preconditioner for Linear Equations in Graph Laplacians (abstract) PRESENTER: Junyuan Lin |