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Reports (Research Report) Year : 1997

Non Overlapping Domain Decomposition for Singularly Perturbed Elliptic Boundary Value Problems

Marc Garbey
  • Function : Author
Laurence Viry
  • Function : Author
  • PersonId : 756531
  • IdRef : 081187793

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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Dates and versions

inria-00073552 , version 1 (24-05-2006)

Identifiers

  • HAL Id : inria-00073552 , version 1

Cite

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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