Summary: On a Parallel Implementation of the Mortar
Gassan S. Abdoulaev \Lambda , Yves Achdou y ,
Yuri A. Kuznetsov \Lambda , Christophe Prud'homme z
We discuss here a parallel implementation of the domain decomposition method based on
the macrohybrid formulation of a second order elliptic equation and on an approximation by
the mortar element method. The discretization leads to an algebraic saddlepoint problem.
An iterative method with a blockdiagonal preconditioner is used for solving the saddle
point problem. A parallel implementation of the method is emphasized. Finally the results
of numerical experiments are presented.
Key words: domain decomposition; mortar finite element method; saddlepoint problem; pre
conditioned iterative method; parallel computing.
Domain decomposition methods for solving the linear systems arising from the approximations
of elliptic partial differential equations have been studied intensively by many researchers all
over the world, motivated by the need to develop new algorithms for parallel computers.
In this paper, we deal with an algorithm for solving the linear systems arising from the
mortar method, introduced by C. Bernardi, Y. Maday and A. Patera . The main feature
of this method is that the continuity condition at the interface of the subdomains is treated