An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids

Antonietti, Poala F.; Houston, Paul; Pennesi, Giorgio; Suli, Endre

Abstract

In this article we design and analyze a class of two-level non-overlapping additive Schwarz preconditioners for the solution of the linear system of equations stemming from discontinuous Galerkin discretizations of second-order elliptic partial differential equations on polytopic meshes. The preconditioner is based on a coarse space and a non-overlapping partition of the computational domain where local solvers are applied in parallel. In particular, the coarse space can potentially be chosen to be non-embedded with respect to the finer space; indeed it can be obtained from the fine grid by employing agglomeration and edge coarsening techniques. We investigate the dependence of the condition number of the preconditioned system with respect to the diffusion coefficient and the discretization parameters, i.e., the mesh size and the polynomial degree of the fine and coarse spaces. Numerical examples are presented which confirm the theoretical bounds.

Citation

Antonietti, P. F., Houston, P., Pennesi, G., & Suli, E. (2020). An agglomeration-based massively parallel non-overlapping additive Schwarz preconditioner for high-order discontinuous Galerkin methods on polytopic grids. Mathematics of Computation, 89, 2047-2083. https://doi.org/10.1090/mcom/3510

• Journal Article Type: Article
• Acceptance Date: Nov 7, 2019
• Online Publication Date: Feb 18, 2020
• Publication Date: Feb 18, 2020
• Deposit Date: Nov 7, 2019
• Publicly Available Date: Nov 11, 2019
• Journal: Mathematics of Computation
• Print ISSN: 0025-5718
• Electronic ISSN: 1088-6842
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 89
• Pages: 2047-2083
• DOI: https://doi.org/10.1090/mcom/3510
• Keywords: Algebra and Number Theory; Applied Mathematics; Computational Mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/3078436
• Publisher URL: https://www.ams.org/journals/mcom/0000-000-00/S0025-5718-2020-03510-8/
• Contract Date: Nov 7, 2019