A domain splitting method for heat conduction problems in composite materials

Friedrich Karl Hebeker

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 1, page 47-62
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Hebeker, Friedrich Karl. "A domain splitting method for heat conduction problems in composite materials." ESAIM: Mathematical Modelling and Numerical Analysis 34.1 (2010): 47-62. <http://eudml.org/doc/197468>.

@article{Hebeker2010,
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. },
author = {Hebeker, Friedrich Karl},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Fibre layers of adaptive material; homogenization; heat conduction; finite element method; noniterative overlapping domain decomposition.; composite materials; layered subdomains; noniterative overlapping domain decomposition; convergence; error estimates; linear evolutionary heat equation; finite elements; domain splitting method; numerical experiments},
language = {eng},
month = {3},
number = {1},
pages = {47-62},
publisher = {EDP Sciences},
title = {A domain splitting method for heat conduction problems in composite materials},
url = {http://eudml.org/doc/197468},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Hebeker, Friedrich Karl
TI - A domain splitting method for heat conduction problems in composite materials
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 1
SP - 47
EP - 62
AB - 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.
LA - eng
KW - Fibre layers of adaptive material; homogenization; heat conduction; finite element method; noniterative overlapping domain decomposition.; composite materials; layered subdomains; noniterative overlapping domain decomposition; convergence; error estimates; linear evolutionary heat equation; finite elements; domain splitting method; numerical experiments
UR - http://eudml.org/doc/197468
ER -

References

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