Joar Bagge: Compression of matrices based on fundamental solutions of elliptic PDEs

Abstract: We consider methods for solving elliptic PDEs based on the fundamental solution of the differential operator. Examples include boundary integral methods (BIM) and the method of fundamental solutions (MFS). These methods lead to dense linear systems in which the matrix entries are point values of the fundamental solution. Often, the matrix has a rank structure, with the off-diagonal blocks being of low rank, which can be exploited for compression. The compression technique in this talk is based on skeletonization and leads to a well-conditioned system amenable to iterative solvers and fast methods. We show numerical examples where the compression reduces the number of unknowns by over 90%.