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

Maksymilian Dryja 1 , Juan Galvis 2  and Marcus Sarkis 3
  • 1 Department of Informatics, Vistula University, Stoklosy 3, 02-787 Warsaw, Poland
  • 2 Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia
  • 3 Department of Mathematical Sciences at Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA

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.

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CMAM considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. The journal is interdisciplinary while retaining the common thread of numerical analysis, readily readable and meant for a wide circle of researchers in applied mathematics.

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