Une methode de decomposition de domaines multifrontale multiniveaux
Keywords:
finite element method, domain decomposition, multilevel decompisition, multifrontal methodAbstract
The developpement of multiprocessor computers has led to a new interest in domain decomposition methods. The goal of this article is to present a multilevel domain decomposition algorithm for the finite element method using a direct solver on the interface problems at each level. In order to reduce the cost of building the inverse of the rigidity matrices of each subdomain, a multifrontal method is used. After a brief description of the Schur complement method and its classical implementation, the multifrontal method is presented in detail. A comparison of theoretical number of operations and measured execution times between these two implementations is given. In the second part of the article, the influence of two parameters is studied : the number of subdomains and the number of decomposition levels. Finally, a comparison between the multifrontal domain decomposition method and a method without decomposition is provided.
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References
[Debruyne 83] G. DEBRUYNE, Y. WADIER, "Barrage de Garrabet: un calcul
tridimensionnel par elements finis", note E.D.F. Hi/4374-07
[Duff] I. Duff, A. ERISMANN, J. REID, Direct methods for sparse matrices, Clarandon Press
Oxford
[Escaig 92] Y. ESCAIG, Compte rendu de Ia rencontre avec M. DELCEY de
FRAMASOFf +CSI a Lyon, compte rendu interne E.D.F. n°866-07
[Escaig 93] Y. ESCAIG, M. VAYSSADE, G. TOUZOT, "Automatisation de Ia decomposition
de domaines dans un logiciel de calcul par elements finis", Actes du Colloque National
en calcul des Structures, Vol. 2, pp 847-873, Hermes (1993)
[Escaig 94] Y. ESCAIG, M. VAYSSADE, G. TOUZOT, "Parallelization of a multilevel domain
decomposition", a paraitre dans Computing Systems in Engineering
[Imbert 79] J.F. IMBERT, Analyse des structures par elements finis, Ecole Nationale
Superieure de l'Aeronautique et de l'espace, Cep(ldues Editions
[Irons 69] B.M. IRONS "A frontal solution program for finite element analysis", Int. Jour.
Num. Meth. Eng., Vol 2, pp 5-32 (1970)
[Keunings 92] R. KEUNINGS, 0. ZONZ, R. AGGARWAL "Parallel algorithms in
computational Rheology", in Xlth International Congress on Rheology, Brussels, Ed
P. Moldenaers, R. Keunings, Elsevier, 274-276 (1992)
[Lesoinne 91] M. LESOINNE, C. FARHAT, M. GERADIN, "ParallelNector improvements of
the frontal method", Int. J. Numer. Meth. Engrg., Vol 32, pp1267-1282 (1991)
[Le Tallec 90] P. LE TALLEC, Y-H. De ROECK, M. VJDRASCU "Domain decomposition
methods for large linearly elliptic three dimensional problems", Rapport de recherche
de l'INRIA n°1182 (1990)
[Roge 93] C. ROGE, F-X Roux "Methodes de calcul des structures composites par sousdomaines
sur calculateurs MIMD", Actes du Colloque National en calcul des Structures,
Vol. 2, pp 920-927, Hermes (1993)
[Roux 89] F-X. Roux "Methode de decomposition de domaine a !'aide de multiplicateurs
de Lagrange et application a Ia resolution en parallele des equations de l'elasticite
lineaire", These de l'Universite de Paris 6 (1989)
[Sloan 89] S. SLOAN, "A Fortran program for profile and wavefront reduction", Int. J.
Numer. Meth. Engrg., Vol 28, pp 2651-2679 (1989)
[Schrem 89] E. SCHREM Handbook for linear static analysis, INTES Publication UM 404
Rev C (1989)
