CM2021: 20TH COPPER MOUNTAIN CONFERENCE ON MULTIGRID METHODS
PROGRAM

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

Wednesday, March 24th

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16:00-18:00 Session 1: Multigrid - the Fundamentals (Luke Olson)

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.

Location: Bighorn A
Thursday, March 25th

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16:00-18:00 Session 2: Algebraic Multigrid and Advanced Topics (James Brannick and Karsten Kahl)

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.

Location: Bighorn A
Friday, March 26th

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16:00-18:00 Session 3: Parallel Multigrid (Ulrike Yang)

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).

Location: Bighorn A
Monday, March 29th

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15:00-16:40 Session 4A: Algebraic multigrid (Part 1 of 2)
Location: Bighorn A
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)
15:00-16:40 Session 4B: Multigrid, DD, and saddle-point systems
Location: Bighorn B
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)
16:15
Multigrid Methods for Elliptic Optimal Control Problems (abstract)
PRESENTER: Sijing Liu
16:40-17:20Break
17:20-19:00 Session 5A: Machine learning and multilevel methods (Part 1 of 2)
Chair:
Location: Bighorn A
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
17:20-19:00 Session 5B: Design and performance for emerging architectures
Location: Bighorn B
17:20
Porting an aggregation-based algebraic multigrid method on GPU (abstract)
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)
19:00-19:15Break
Tuesday, March 30th

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15:00-16:40 Session 6A: Structured and matrix-free methods (Part 1 of 2)
Location: Bighorn A
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
15:00-16:40 Session 6B: Applications and coupled physics problems (Part 1 of 2)
Location: Bighorn B
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)
16:15
A local Fourier analysis of low order preconditioners for the Stokes equations (abstract)
PRESENTER: Alexey Voronin
16:40-17:20Break
17:20-19:00 Session 7A: Machine learning and multilevel methods (Part 2 of 2)
Location: Bighorn A
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)
18:35
Multiscale training for Physics-informed Neural Networks (abstract)
PRESENTER: Ravi G. Patel
17:20-19:00 Session 7B: Multilevel, multi-model, and mixed methods
Location: Bighorn B
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)
18:10
p-refined Multilevel Quasi-Monte Carlo with Locally Nested Random Field Evaluation Points Applied to a Geotechnical Engineering Problem (abstract)
18:35
Effective material parameters from microstructures constructed using the planar Boolean model (abstract)
19:00-19:15Break
Wednesday, March 31st

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15:00-17:05 Session 8A: Parallel time integration
Location: Bighorn A
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)
15:00-17:05 Session 8B: Algebraic multigrid, indefinite problems, and matrix exponentials
Chair:
Location: Bighorn B
15:00
Scalable minimum-residual multigrid solver for wave propagation (abstract)
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
17:05-17:45Break
17:45-19:00 Session 9: Student competition winners
Location: Bighorn A
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
19:00-19:15Break
Thursday, April 1st

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15:00-16:40 Session 10A: Algebraic multigrid (Part 2 of 2)
Chair:
Location: Bighorn A
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)
15:00-16:40 Session 10B: Multigrid and factorization methods
Location: Bighorn B
15:00
Nonnegative Unimodal Matrix Factorization (abstract)
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
17:20-19:00 Session 11A: Structured and matrix-free methods (Part 2 of 2)
Location: Bighorn A
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)
18:35
Optimization of two-level methods for DG discretizations of reaction-diffusion equations (abstract)
17:20-19:00 Session 11B: Multigrid and Schwarz methods
Location: Bighorn B
17:20
Additive Schwarz methods for serendipity elements (abstract)
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)
19:00-19:15Break
Friday, April 2nd

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15:00-17:20 Session 12A: Multigrid smoothers
Location: Bighorn A
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
15:00-16:40 Session 12B: Applications and coupled physics problems (Part 2 of 2)
Location: Bighorn B
15:00
FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica (abstract)
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
16:40-17:20Break
17:20-19:00 Session 13: Multigrid, analysis, and LFA
Location: Bighorn A
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)
17:45-19:00 Session 14: Graph problems
Location: Bighorn B
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
19:00-19:15Break