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A domain splitting method for heat conduction problemsin composite materials

Published online by Cambridge University Press:  15 April 2002

Friedrich Karl Hebeker
Friedrich Karl Hebeker*
Affiliation:
Fachbereich Mathematik, Justus-Liebig-Universit t Gießen, Arndtstr. 2, 35392 Gießen, Germany. (friedrich.k.hebeker@math.uni-giessen.de)
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Abstract

We consider a domain decomposition method for some unsteadyheat conduction problem in composite structures.This linear model problem is obtained by homogenization of thin layersof fibres embedded into some standard material.For ease of presentation we consider the case of two space dimensions only.The set of finite element equations obtained by the backward Euler schemeis parallelized in a problem-oriented fashion by some noniterative overlappingdomain splitting method,eventually enhanced by inexpensive local iterationsto reduce the overlap.We present a detailed convergence analysis of this algorithmwhich is particularly well appropriate to handle fibre layersof nonlinear material.Special emphasis is to take into account the specific regularity propertiesof the present mathematical model.Numerical experiments show the reliability of the theoretical predictions.

Keywords

Fibre layers of adaptive materialhomogenizationheat conductionfinite element methodnoniterative overlapping domain decomposition.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 1 , January 2000 , pp. 47 - 62
Copyright
© EDP Sciences, SMAI, 2000

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