Solving Signorinis’ Problem on the Basis of Domain Decomposition Operators

Joachim Schöberl Johannes Kepler Universität Linz, Austria

Abstract

In the last years a couple of very efficient computable operators for domain decomposition have been developed. The idea is to decouple the linear system into inner Dirichlet subproblems and the Schur-complement problem at the boundary.

The Finite Elemente Discretization of Signorinis’ Problem leaves to a constrained finite dimensional minimization problem. This problem can be solved by the projection method, which is very similar to Richardson iteration. Because of the slow convergence rate on fine meshes preconditioning has to be applied. The application of the preconditioner has to be fast computable, the relative condition number of the system matrix with respect to the preconditioner has to be small and the projection onto the set of feasible elements has to be fast computable. It is shown how to build a preconditioner of optimal complexity on the basis of Domain Decomposition.