Une méthode de décomposition de domaines multifrontale multiniveaux

ABSTRACT 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.