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A domain splitting method for heat conduction problems in 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. ([email protected])
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Abstract

We consider a domain decomposition method for some unsteady heat conduction problem in composite structures. This linear model problem is obtained by homogenization of thin layers of 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 scheme is parallelized in a problem-oriented fashion by some noniterative overlapping domain splitting method, eventually enhanced by inexpensive local iterations to reduce the overlap. We present a detailed convergence analysis of this algorithm which is particularly well appropriate to handle fibre layers of nonlinear material. Special emphasis is to take into account the specific regularity properties of 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.
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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