Work

A nonoverlapping spectral additive Schwarz method for interior penalty discontinuous Galerkin discretizations of Anisotropic Elliptic Problems

Year: 2026

Type: preprint

Abstract: We design and analyze a nonoverlapping additive Schwarz preconditioner for interior penalty discontinuous Galerkin discretizations of anisotropic elliptic problems. The preconditioned method coupled with a Krylov subspace iteration is shown to be independent of the highly discontinuous (and anisotropic) jump coefficients as well as the subdomain size. To increase efficacy, various auxiliary spaces are considered to reduce the size of the coarse grid operator. We demonstrate how to modify the additive Schwarz preconditioner such that it is applicable to the nonsymmetric IPDG schemes. Several numerical experiments verify the theory and validate the robustness of the preconditioner.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.30639

Authors: Fabien, Maurice S., Liu, Sijing, Sarkis, Marcus

Institutions: SUNY Polytechnic Institute, University of Wisconsin–Madison, Massachusetts Institute of Technology, Worcester Polytechnic Institute

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214671915

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