FMM accelerated BEM for 3D Laplace & Helmholtz equations

We describe development of a fast multipole method accelerated iterative solution of boundary element equations for large problems involving hundreds of thousands elements for the Laplace and Helmholtz equations in 3D. The BEM requires several approximate computations (numerical quadrature, approximations of the boundary shapes using elements) and the convergence criterion for iterative computation. When accelerated using the FMM, these different errors must all be chosen in a way that on the one hand excess work is not done and on the other that the error achieved by the overall computation is acceptable. We show results of developed and tested solvers for the boundary value problems for the Laplace and Helmholtz equations using the BEM/GMRES/FMM. The performance tests for both were conducted in the rangeN . 10 and kD . 150 (in the Helmholtz case) and showed good performance close to theoretical expectations.