New Analysis of Overlapping Schwarz Methods for Vector Field Problems in Three Dimensions with Generally Shaped Domains

2024/04/18 by Duk‐Soon Oh, Oh, Duk-Soon, Shangyou Zhang +1 · 1 citation
Engineering · Mathematics · #65F08 #65F10 #65N30 #65N55 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2404.11986

openalex publication_date 2024/04/18 · openalex created_date 2024/04/20 · openalex updated_date 2026/07/28

Abstract

This paper introduces a novel approach to analyzing overlapping Schwarz methods for Nédélec and Raviart--Thomas vector field problems. The theory is based on new regular stable decompositions for vector fields that are robust to the topology of the domain. Enhanced estimates for the condition numbers of the preconditioned linear systems are derived, dependent linearly on the relative overlap between the overlapping subdomains. Furthermore, we present the numerical experiments which support our theoretical results.

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• Multiscale model reduction and two-level Schwarz preconditioner for H(curl) elliptic problems

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