A Parallel Interface Preconditioner for the Mortar Element Method in Case of Jumping Coefficients

The paper is devoted to designing an interface preconditioner for the mortar element method. After brief overview of the problem in Introduction, we discuss the mortar element method with different types of the Lagrange multiplier spaces. Next, we consider the domain decomposition technique for the solution of mortar element systems and outline the general framework of the solution of saddle-point systems which result from the mortar element system. In the last two sections, we constuct the interface preconditioner for the saddle-point Schur complement, which is the goal of the paper, and we present numerical experiments illustrating the basic properties of the interface preconditioner. Designing the interface preconditioner is one of the most difficult problems in the mortar element method. In this paper we continue development of the DirichletDirichlet preconditioner [DA99, KV99]. We extend the method to the case of arbitrary type of Lagrange multiplier space and large jumps of coefficients. The proposed algorithm possesses natural parallelism. It is illustrated on a set of numerical experiments.