A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients

A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients

We propose a BDDC preconditioner for the rotated Q1 finite element method for second order elliptic equations with piecewise but discontinuous coefficients. In the framework of the standard additive Schwarz methods, we describe this method by a complete variational form. We show that our method has...

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Main Author: Yaqin Jiang
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/859424
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spelling doaj-fc95e4c79a26456da7ed0fa71c5a738f2020-11-24T21:17:44ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/859424859424A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous CoefficientsYaqin Jiang0School of Sciences, Nanjing University of Posts and Telecommunications, Nanjing 210046, ChinaWe propose a BDDC preconditioner for the rotated Q1 finite element method for second order elliptic equations with piecewise but discontinuous coefficients. In the framework of the standard additive Schwarz methods, we describe this method by a complete variational form. We show that our method has a quasioptimal convergence behavior; that is, the condition number of the preconditioned problem is independent of the jumps of the coefficients and depends only logarithmically on the ratio between the subdomain size and the mesh size. Numerical experiments are presented to confirm our theoretical analysis.http://dx.doi.org/10.1155/2014/859424
collection DOAJ
language English
format Article
sources DOAJ
author Yaqin Jiang
spellingShingle Yaqin Jiang
A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients
Journal of Applied Mathematics
author_facet Yaqin Jiang
author_sort Yaqin Jiang
title A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients
title_short A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients
title_full A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients
title_fullStr A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients
title_full_unstemmed A BDDC Preconditioner for the Rotated Q1 FEM for Elliptic Problems with Discontinuous Coefficients
title_sort bddc preconditioner for the rotated q1 fem for elliptic problems with discontinuous coefficients
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2014-01-01
description We propose a BDDC preconditioner for the rotated Q1 finite element method for second order elliptic equations with piecewise but discontinuous coefficients. In the framework of the standard additive Schwarz methods, we describe this method by a complete variational form. We show that our method has a quasioptimal convergence behavior; that is, the condition number of the preconditioned problem is independent of the jumps of the coefficients and depends only logarithmically on the ratio between the subdomain size and the mesh size. Numerical experiments are presented to confirm our theoretical analysis.
url http://dx.doi.org/10.1155/2014/859424
work_keys_str_mv AT yaqinjiang abddcpreconditionerfortherotatedq1femforellipticproblemswithdiscontinuouscoefficients
AT yaqinjiang bddcpreconditionerfortherotatedq1femforellipticproblemswithdiscontinuouscoefficients
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