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Abstract - Boundary Element Domain Decomposition Methods

Author: Olaf Steinbach

Title of the contribution: Boundary Element Domain Decomposition Methods

Abstract:
In this talk we give an overview on domain decomposition methods via boundary elements. Appropriate boundary integral equations are used to describe the local Dirichlet to Neumann map, or the inverse Neumann to Dirichlet map, respectively.

For the discrisation of the local subproblems a Galerkin boundary element method based on several representations of the Steklov-Poincaré operator are discussed, in particular, corresponding stability and error estimates are given.

For the parallel solution of the resulting linear systems we discuss different strategies. Starting from a Schur complement conjugate gardient scheme we als consider the equivalent coupled block skew-symmetric positive definite system, which can be solved via a transformation due to Bramble and Pasciak. Alternatively, using a tearing and interconnecting approach, corresponding linear systems involving the dual Lagrange parameters can be considered as well. All of the above solution strategies involve the need of efficient local and global preconditioners where some appropriate choices are given.

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