0727 Multi-level iterative solvers for finite element systems

  • Matthias Mayr, University Of The Bundeswehr Munich
  • Martin Kronbichler, Uppsala University
  • Santiago Badia, Monash University

In many scientific and engineering applications, finite element discretizations (also in a broad sense, e.g. including DG, VEM, HDG, etc.) result in large sparse linear systems of equations with millions or even billions of unknowns. Such systems are intractable for out-of-the-box direct solvers and require the use of iterative solution methods. Multi-level approaches are the most widespread class of solvers and preconditioners in use today when it comes to scalability on the largest supercomputers and robustness for differential operators with strong elliptic character. Essentially, these approaches are based on the construction of coarse approximations of the original fine-level problem.

This minisymposium addresses the most important and active research topics for scalable multi-level iterative solvers and preconditioners for sparse linear systems in the context of finite element and discontinuous Galerkin discretizations, including
- domain decomposition solvers,
- geometric and algebraic multi-grid methods,
- p-multigrid techniques,
- matrix-based and matrix-free algorithms,
- adaptive coarse spaces, coarse spaces with additional constraints.

The minisymposium invites interdisciplinary contributions with a wide range of focus, including directions such as
- single and coupled multi-field problems,
- high-order and spectral element discretizations
- high-performance computing,
- emerging hardware architecture, e.g. accelerator devices,
- applications in natural sciences, engineering, and biomedicine.

The aim of this minisymposium is to provide a forum for researchers to discuss promising developments and advances in multi-level solvers for large sparse linear systems of equations as well as challenges related to the present and emerging computing hardware. We also want to facilitate an open discussion on differences and commonalities among various classes of multi-level solvers.

© WCCM-APCOM 2022. All Rights Reserved.