Efficient preconditioners for boundary element matrices based on grey-box algebraic multigrid methods

摘要

This paper is concerned with the iterative solution of the boundary element equations arising from standard Galerkin boundary element discretizations of first-kind boundary integral operators of positive and negative order. We construct efficient preconditioners on the basis of so-called grey-box algebraic multigrid methods that are well adapted to the treatment of boundary element matrices. In particular, the coarsening is based on an auxiliary matrix that represents the underlying topology in a certain sense. This auxiliary matrix is additionally used for the construction of the smoothers and the transfer operators. Finally, we present the results of some numerical studies that show the efficiency of the proposed algebraic multigrid preconditioners.