Chinese Annals of Mathematics, Series B

, Volume 36, Issue 5, pp 803–812 | Cite as

Two-level additive Schwarz methods using rough polyharmonic splines-based coarse spaces

Article

Abstract

This paper introduces a domain decomposition preconditioner for elliptic equations with rough coefficients. The coarse space of the domain decomposition method is constructed via the so-called rough polyharmonic splines (RPS for short). As an approximation space of the elliptic problem, RPS is known to recover the quasi-optimal convergence rate and attain the quasi-optimal localization property. The authors lay out the formulation of the RPS based domain decomposition preconditioner, and numerically verify the performance boost of this method through several examples.

Keywords

Numerical homogenization Domain decomposition Two-level Schwarz additive preconditioner Rough polyharmonic splines 

2000 MR Subject Classification

35B27 41A15 65N55 

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Copyright information

© Fudan University and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Mathematical Center for Interdisciplinary Research, School of Mathematical SciencesSoochow UniversitySuzhou, JiangsuChina
  2. 2.Institute of Natural Sciences and Department of Mathematics, Ministry of Education Key Laboratory of Scientific and Engineering ComputingShanghai Jiaotong UniversityShanghaiChina

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