An interative and multigrid solution of boundary integral equations

An iterative method for solving the boundary integral equations of mixed-type boundary value problems is presented. A sequence consisting of pure Dirichlet and pure Neumann problems is defined, such that it converges to the solution of the original mixed problem in the Sobolev space H1(Ω, Δ). To speed up the iteration, multigrid tools are used in solving the above subproblems. The resulting method requires only O(N2) operations, where N is the number of boundary nodes. This implies that the computational cost of the proposed method is significantly less than that of the traditional, direct solvers of boundary integral equations, in which O(N3) operations are needed.