Non Overlapping Domain Decomposition for Singularly Perturbed Elliptic Boundary Value Problems

Abstract : We analyze the Funaro-Quarteroni alternative procedure for the solution of singular perturbation problems. We show that for an appropriate choice of the domain decomposition, one obtains a fast convergent iterative scheme with {\it no relaxation} that resolves the boundary layers. The convergence is superlinear with respect to the singular perturbation parameter $\epsilon$ in the following sense: the amplification factor is $o(\epsilon)$. We give sharp estimates of the interface position and convergent rates for an homogeneous domain decomposition in one dimensional space as well as in two dimensional space problems on a disk. We extend our results to heterogeneous domain decomposition arising in a simplified model of an electromagnetic problem. We report on implementation results with finite difference approximations and finite element codes ({\it Modulef})
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Rapport
[Research Report] RR-3137, INRIA. 1997, pp.45
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https://hal.inria.fr/inria-00073552
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Soumis le : mercredi 24 mai 2006 - 13:10:47
Dernière modification le : samedi 17 septembre 2016 - 01:06:53
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:50:02

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Marc Garbey, Laurence Viry, Olivier Coulaud. Non Overlapping Domain Decomposition for Singularly Perturbed Elliptic Boundary Value Problems. [Research Report] RR-3137, INRIA. 1997, pp.45. 〈inria-00073552〉

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