A domain splitting method for heat conduction problems in composite materials

Free access article

Issue		ESAIM: M2AN Volume 34, Number 1, January-February 2000


Page(s)		47 - 62
DOI		10.1051/m2an:2000130

DOI: 10.1051/m2an:2000130
M2AN, Vol. 34, N $^{\rm o}$ 1, 2000, pp. 47-62

A domain splitting method for heat conduction problems
in composite materials

Friedrich Karl Hebeker
Fachbereich Mathematik, Justus-Liebig-Universität Gießen, Arndtstr. 2, 35392 Gießen, Germany. (friedrich.k.hebeker@math.uni-giessen.de)

Received: April 15, 1999

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 and phrases: Fibre layers of adaptive material, homogenization, heat conduction, finite element method, noniterative overlapping domain decomposition.

AMS Subject Classification: 80A22, 65M

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