CM2023: 21ST COPPER MOUNTAIN CONFERENCE ON MULTIGRID METHODS
PROGRAM

Days: Sunday, April 16th Monday, April 17th Tuesday, April 18th Wednesday, April 19th Thursday, April 20th

Sunday, April 16th

View this program: with abstractssession overviewtalk overview

10:00-12:00 Session 1: Multigrid - the Fundamentals (Hans De Sterck)

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 C-1
14:00-16:00 Session 2: Algebraic Multigrid and Advanced Topics (James Brannick)

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 C-1
16:30-18:00 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.

Location: Bighorn C-1
Monday, April 17th

View this program: with abstractssession overviewtalk overview

07:30-08:30Breakfast Buffet
08:00-10:05 Session 4A: Parallel time integration (Part 1 of 3)
Location: Bighorn C
08:00
Parameterized Runge-Kutta Integrators on Coarse Levels in Multigrid Reduction in Time (abstract)
PRESENTER: Ryo Yoda
08:25
Accelerating the Maximum Likelihood Ensemble Smoother by Multigrid-in-Time for Data Assimilation (abstract)
08:50
Optimizing the Space-Time Multigrid Algorithm with Block-Jacobi Smoother (abstract)
09:15
Optimized Schwarz Method in Time for Transport Control (abstract)
PRESENTER: Duc Quang Bui
09:40
Multigrid in Time for Time-Periodic Parabolic Evolution Problems (abstract)
08:00-10:05 Session 4B: Artificial intelligence and multilevel methods (Part 1 of 3)
Location: Bighorn B
08:00
A Hybrid Iterative Numerical Transferable Solver (HINTS) for PDEs Based on Deep Operator Network and Relaxation Methods (abstract)
PRESENTER: Enrui Zhang
08:25
On the Geometry Transferability of the Hybrid Iterative Numerical Solver for Differential Equations (abstract)
PRESENTER: Somdatta Goswami
08:50
Optimal Approximation Rates for Deep ReLU Neural Networks on Sobolev Spaces (abstract)
09:15
MGiaD: Multigrid in all dimensions. Efficiency and robustness of convolutional neural networks by weight-sharing and coarsening in resolution and channel dimensions (abstract)
09:40
Gradient-based optimization of sparse relaxation schemes (abstract)
PRESENTER: Nicolas Nytko
10:05-10:25Coffee and Tea Break
10:25-12:30 Session 5A: Parallel time integration (Part 2 of 3)
Location: Bighorn C
10:25
A 2-Level Domain Decomposition Preconditioner for KKT Systems with Heat-Equation Constraints (abstract)
10:50
Analysis of ParaDiag and ParaOpt for time-parallel linear optimal control (abstract)
PRESENTER: Arne Bouillon
11:15
Paraopt algorithm and Runge-Kutta methods (abstract)
11:40
Discrete Event-Handling for Spectral Deferred Corrections (abstract)
PRESENTER: Lisa Wimmer
12:05
Parallel Space-Time Finite Element Method for the Eddy Current Problem in Moving Domains (abstract)
PRESENTER: Mario Gobrial
10:25-12:30 Session 5B: Applications (Part 1 of 3)
Location: Bighorn B
10:25
Hybridised multigrid for compatible finite element discretisations in climate and weather prediction (abstract)
PRESENTER: Eike Mueller
10:50
Irksome: Automated Runge-Kutta methods and monolithic multigrid for time-stepping PDE (abstract)
PRESENTER: Robert Kirby
11:15
Monolithic Multigrid Preconditioners for High-Order Discretizations of the Navier-Stokes Equations (abstract)
PRESENTER: Scott MacLachlan
11:40
Preconditioning for implicit Runge-Kutta methods for hyperbolic pde problems (abstract)
PRESENTER: Aman Rani
12:05
Overview of the WarpX code: numerical methods and algorithms, software engineering strategies, and applications (abstract)
PRESENTER: Edoardo Zoni
12:30-16:00Lunch Break
14:30-16:00 Session 6: Multigrid Methods for Coupled Systems (Scott MacLachlan)

Developing effective multigrid methods for systems of PDEs generally requires somewhat different multigrid components than are typically used for scalar elliptic PDEs.  In this tutorial, we discuss common uses of multigrid for solving such systems and the components of effective multigrid methods for them.  We will discuss block factorization schemes, that apply multigrid methods to component blocks of the system, and monolithic multigrid methods, that apply specialized relaxation schemes to the coupled systems directly.

Location: Bighorn C
16:00-16:30Coffee and Tea Break
16:30-18:35 Session 7: Algebraic multigrid
Chair:
Location: Bighorn B
16:30
Toward a multilevel method for the Helmholtz equation (abstract)
16:55
Monolithic Algebraic Multigrid Preconditioners for the Stokes Equations (abstract)
PRESENTER: Alexey Voronin
17:20
Well-balanced aggregation for algebraic multigrid (abstract)
PRESENTER: Luke Olson
17:45
Improving AMG Strength of Connection (abstract)
PRESENTER: Wayne Mitchell
18:10
Compatible Relaxation and Block Smoothers for AMG (abstract)
PRESENTER: Taoli Shen
Tuesday, April 18th

View this program: with abstractssession overviewtalk overview

07:30-08:30Breakfast Buffet
08:00-10:05 Session 8A: Applications (Part 2 of 3)
Location: Bighorn C
08:00
Scalable DPG multigrid solver with applications in wave propagation (abstract)
08:25
Generalizing Approximate Ideal Restriction (AIR) Algebraic Multigrid (abstract)
PRESENTER: Jacob Schroder
08:50
Algebraic multigrid methods for non-symmetric problems (abstract)
PRESENTER: Ahsan Ali
09:15
Performance evaluation of a continental-scale, integrated hydrologic model: adventures of a hydrologist in computer science (abstract)
08:00-10:05 Session 8B: Artificial intelligence and multilevel methods (Part 2 of 3)
Location: Bighorn B
08:00
Torchbraid - a framework for layer-parallel training (abstract)
PRESENTER: Jens Hahne
08:25
MG-GNN: Multigrid Graph Neural Networks for Learning Multilevel Domain Decomposition Methods (abstract)
PRESENTER: Ali Taghibakhshi
08:50
Preconditioning for Large Scale Systems based on the HINTS (abstract)
09:15
Data-Driven Approaches for Patch-Based Multigrid Smoothers (abstract)
PRESENTER: Graham Harper
09:40
Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training (abstract)
10:05-10:25Coffee and Tea Break
10:25-12:30 Session 9A: Parallel time integration (Part 3 of 3)
Location: Bighorn C
10:25
Multigrid reduction-in-time for linear acoustics (abstract)
PRESENTER: Oliver Krzysik
10:50
Efficacy of a parareal algorithm for solving highly oscillatory Vlasov-Poisson systems (abstract)
11:15
Multimodel, Multiscale Parallel-in-Time for Kinetic Plasmas (abstract)
PRESENTER: Paul Tranquilli
11:40
Towards fast topology optimisation of transient problems: parallel space-time multigrid (abstract)
12:05
Time-Parallel Multigrid Preconditioning for KKT Systems Arising in Constrained Optimization (abstract)
10:25-12:30 Session 9B: Coupled physics problems (Part 1 of 2)
Location: Bighorn B
10:25
A Two-phases Hybrid Method for Modelling Neutral Particles in the Plasma Edge of a Fusion Device (abstract)
PRESENTER: Vince Maes
10:50
A novel solver technique for anisotropic heat flux in plasma modelling using AIR (abstract)
PRESENTER: Thomas Gregory
11:15
Scalable solvers for multi-ion transport in electrochemistry (abstract)
PRESENTER: Thomas Roy
11:40
Variational modeling of fluid in poroelastic medium (abstract)
12:05
A multigrid method for solving variational inequalities (abstract)
PRESENTER: Hardik Kothari
12:30-16:00Lunch Break
16:00-16:30Coffee and Tea Break
16:30-18:35 Session 10: Multigrid and multilevel methods
Location: Bighorn B
16:30
A Remark on Inter-mesh Transfer Operators of V-scheme Multigrid Method for Shrinking Meshes in One-Dimension (abstract)
16:55
An algorithm for rational approximation of fractional powers of matrices via the reduced basis method (abstract)
PRESENTER: Cheng Zuo
17:20
Discrete Fourier analysis -- A structural approach with applications to local Fourier analysis (abstract)
17:45
MGProx: A nonsmooth multigrid proximal gradient method with adaptive restriction for strongly convex optimization (abstract)
PRESENTER: Hans De Sterck
Wednesday, April 19th

View this program: with abstractssession overviewtalk overview

07:30-08:30Breakfast Buffet
08:00-10:05 Session 11A: Coupled physics problems (Part 2 of 2)
Location: Bighorn C
08:00
Nested Iteration and Nonlinear Methods for Liquid Crystal Shape Optimization Applications (abstract)
PRESENTER: Anca Andrei
08:25
A Micro-Macro Markov Chain Monte Carlo Method with Applications in Molecular Dynamics (abstract)
08:50
A multigrid method for generalized extended magnetohydrodynamics (abstract)
PRESENTER: Raymond Tuminaro
09:15
Towards a scalable fully-implicit VMS formulation for Low Mach compressible visco-resistive MHD for application to MCF in Tokamak relevant geometries (abstract)
09:40
Block Preconditioning for Magnetic Confinement Fusion Relevant Resistive MHD Simulations (abstract)
PRESENTER: Peter Ohm
08:00-10:05 Session 11B: Artificial intelligence and multilevel methods (Part 3 of 3)
Location: Bighorn B
08:00
History Matching Reservoir Models With Many Objective Bayesian Optimization (abstract)
PRESENTER: Steven Samoil
08:25
Multilevel-in-Width Training for Deep Neural Network Regression (abstract)
PRESENTER: Colin Ponce
08:50
On Applying AMG Perspectives to Graph Neural Networks for Image Semantic Segmentation. (abstract)
PRESENTER: Eran Treister
09:15
Reducing operator complexity in Algebraic Multigrid with Machine Learning Approaches (abstract)
PRESENTER: Kai Chang
09:40
Data-driven Multigrid methods based on local Fourier analysis (abstract)
PRESENTER: Rui Peng Li
10:05-10:25Coffee and Tea Break
10:25-12:30 Session 12: Emerging architectures
Chair:
Location: Bighorn B
10:25
Efficient Hybrid Smoothers in AMG and GMRES: Neumann Proxies and Gershgorin's Circle Theorem (abstract)
PRESENTER: Stephen Thomas
10:50
Emerging Architectures Will Be Heterogeneous: What are the Challenges and Opportunities of these Future Architectures (abstract)
11:15
Communication-Computation Overlapping in Parallel Multigrid Methods (abstract)
11:40
Preconditioning Sparse Matrices with Alternating and Multiplicative Operator Splittings (abstract)
PRESENTER: Robert Strzodka
12:05
Distributed Preconditioning for Cardiac Simulations on modern GPUs using BDDC (abstract)
PRESENTER: Fritz Goebel
12:30-16:00Lunch Break
16:00-16:30Coffee and Tea Break
16:30-17:20 Session 13: Student competition winners
Location: Bighorn B
16:30
Multigrid methods using Block Floating Point Arithmetic (abstract)
PRESENTER: Nils Kohl
16:55
A general framework for deriving coarse grid operators for Multigrid Reduction in Time (abstract)
Thursday, April 20th

View this program: with abstractssession overviewtalk overview

07:30-08:30Breakfast Buffet
08:00-09:40 Session 14: Applications (Part 3 of 3)
Location: Bighorn B
08:00
Potential energy principles in networked systems and their connections to optimization problems on graphs (abstract)
08:25
Cascade Prediction in Networks Via Euclidean Embedding (abstract)
08:50
Visualization of simplicial intersections (abstract)
09:15
Numerical study of efficient preconditioners for solving Stokes and Stokes-Brinkman problems in complicated geometries (abstract)
09:40-10:00Coffee and Tea Break
10:00-11:15 Session 15: Multilevel methods for stochastic problems
Location: Bighorn B
10:00
A Multilevel Formulation of EKI and EKS (abstract)
PRESENTER: Toon Ingelaere
10:25
Matrix-based Redistribution for Improved Coarse Level Scaling in Multilevel Markov Chain Monte Carlo (abstract)
10:50
Multilevel methods for optimal control of elliptic equations with stochastic coefficients discretized using stochastic collocation (abstract)