Fast BEM-solution of Laplace problems with H-matrices and ACA

The main problems for applying boundary element methods (BEM) in computational electromagnetism are related to the large memory requirements of the matrices and the convergence of the iterative solver. In this paper, we solve a Laplace problem with mixed boundary conditions by making use of a variational symmetric direct boundary integral equation. The Galerkin discretization results in densely populated matrices that are here compressed by adaptive cross approximation. This leads to an approximation of the underlying BEM-operator by means of so-called hierarchical matrices (H-Matrices). These matrices are then used to construct an effective preconditioner for the iterative solver. Numerical experiments demonstrate the application of the method