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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

4 Issues per year


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Volume 15, Issue 4 (Oct 2015)

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A Deluxe FETI-DP Preconditioner for a Composite Finite Element and DG Method

Maksymilian Dryja / Juan Galvis / Marcus Sarkis
  • Corresponding author
  • Department of Mathematical Sciences at Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA
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Published Online: 2015-09-10 | DOI: https://doi.org/10.1515/cmam-2015-0025

Abstract

In this paper, we present and analyze a FETI-DP solver with deluxe scaling for a Nitsche-type discretization [Comput. Methods Appl. Math. 3 (2003), 76–85], [SIAM J. Numer. Anal. 49 (2011), 1761–1787] based on a discontinuous Galerkin (DG) method for elliptic two-dimensional problems with discontinuous coefficients and non-matching meshes only across subdomains. We establish a condition number estimate for the preconditioned linear system which is scalable with respect to the number of subdomains, is quasi-optimal polylogarithmic with respect to subdomain mesh size, and is independent of coefficient discontinuities and ratio of mesh sizes across subdomain interfaces. Numerical experiments support the theory and show that the deluxe scaling improves significantly the performance over classical scaling.

Keywords: Interior Penalty Discretization; Discontinuous Galerkin; Elliptic Problems with Discontinuous Coefficients; Finite Element Method; FETI-DP Algorithms; Preconditioners; Deluxe

MSC: 65F10; 65N20; 65N30

About the article

Received: 2015-04-14

Revised: 2015-08-08

Accepted: 2015-08-23

Published Online: 2015-09-10

Published in Print: 2015-10-01


Funding Source: NSF MRI

Award identifier / Grant number: DMS-1337943


Citation Information: Computational Methods in Applied Mathematics, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2015-0025.

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