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Article

Hammerbauer, Tomáš ; Dolejší, Vít
Numerical study of two-level additive Schwarz preconditioner for discontinuous Galerkin method solving elliptic problems. (English). In: Chleboun, J., Papež, J., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Hejnice, June 23-28, 2024. , Prague, 2025. pp. 61-71
MSC: 65F08, 65M15, 65N15 | DOI: 10.21136/panm.2024.06
Keywords:
domain decomposition; elliptic partial differential equation; two-level additive Schwarz preconditioner
Summary:
The paper deals with the analysis and numerical study of the domain decomposition based preconditioner for algebraic systems arising from the discontinuous Galerkin (DG) discretization of the linear elliptic problems. We introduce the DG discretization of the model problem and present the spectral $hp$-bound of the corresponding linear algebraic systems. Moreover, we present the two-level additive Schwarz preconditioner together with the theoretical result related to the estimate of the condition number. Finally, we present the numerical experiments supporting the theoretical results and demonstrate the efficiency of this approach for the solution of nonlinear problems.
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