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- Title
An algebraic multigrid method for elasticity based on an auxiliary topology with edge matrices.
- Authors
Kogler, Lukas; Schöberl, Joachim
- Abstract
This article introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second‐order partial differential equations. Based on a discrete energy made up of edge and vertex contributions, we are able to develop coarsening criteria that guarantee two‐level convergence even for systems of equations such as linear elasticity. This energy also allows us to construct prolongations with prescribed sparsity pattern that still preserve kernel vectors exactly. These allow for a straightforward optimization that simplifies parallelization and reduces communication on coarse levels. Numerical experiments demonstrate efficiency and robustness of the method and scalability of the implementation.
- Subjects
ALGEBRAIC multigrid methods; ELLIPTIC differential equations; MULTIGRID methods (Numerical analysis); TOPOLOGY; ELASTICITY; LINEAR equations
- Publication
Numerical Linear Algebra with Applications, 2022, Vol 29, Issue 1, p1
- ISSN
1070-5325
- Publication type
Academic Journal
- DOI
10.1002/nla.2408