# A domain splitting method for heat conduction problems in composite materials

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topHebeker, 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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- Yu.A. Kuznetsov, Overlapping domain decomposition methods for finite element problems with singular perturbed operators. in Domain decomposition Methods for Partial differential equations, R. Glowinski et al. Eds., SIAM, Philadelphia. Proc. of the 4th Intl. Symp. (1991) 223-241 Zbl0766.65089
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