An Algebraic Local Generalized Eigenvalue in the Overlapping Zone Based Coarse Space : A first introduction

Nicole Spillane; Victorita Dolean; Patrice Hauret; Frédéric Nataf; Clemens Pechstein; Robert Scheichl

hal-00630892, version 1

An Algebraic Local Generalized Eigenvalue in the Overlapping Zone Based Coarse Space : A first introduction

Nicole Spillane () ¹, Victorita Dolean () ², Patrice Hauret () ³, Frédéric Nataf () ¹, Clemens Pechstein () ⁴, Robert Scheichl () ⁵

(2011-10-11)

Abstract: Coarse spaces are instrumental in obtaining scalability for domain decomposition methods. However, it is known that most popular choices of coarse spaces perform rather weakly in presence of heterogeneities in the coefficients in the partial differential equations, especially for systems. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems which isolate the terms responsible for slow convergence. We give a general theoretical result and then some numerical examples on a heterogeneous elasticity problem.

1: Laboratoire Jacques-Louis Lions (LJLL)
CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI
2: Laboratoire Jean Alexandre Dieudonné (JAD)
CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS]
3: Centre de Technologie de Ladoux
Société Michelin
4: Institute of Computational Mathematics
Johannes Kepler Universität Linz
5: Department of Mathematical Sciences - University of Bath
University of Bath

hal-00630892, version 1
http://hal.archives-ouvertes.fr/hal-00630892
oai:hal.archives-ouvertes.fr:hal-00630892
From: Frédéric Nataf <>
Submitted on: Tuesday, 11 October 2011 09:27:38
Updated on: Tuesday, 25 October 2011 17:30:57

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