Summary: On a Parallel Implementation of the Mortar
Element Method
Gassan S. Abdoulaev \Lambda , Yves Achdou y ,
Yuri A. Kuznetsov \Lambda , Christophe Prud'homme z
Abstract
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.
1 Introduction
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 [11]. The main feature
of this method is that the continuity condition at the interface of the subdomains is treated

Source: Achdou, Yves - Laboratoire Jacques-Louis Lions, Université Pierre-et-Marie-Curie, Paris 6

Collections: Mathematics