Laplace's equation and the Dirichlet-Neumann map in multiply connected domains
The authors investigate a new integral equation method for the solution of the Dirichlet problem in multiply connected domains. This new formulation is combined with the fast multipole method to produce an algorithm capable of solving the Laplace equation in domains with hundreds of distinct boundary components. The asymptotic CPU time requirements of the authors' scheme are of order \(O(N+M)\) in the unpreconditioned mode and of order \(O(N+M^ 3)\) in the preconditioned mode, where \(N\) is the total number of points in the boundary condition and \(M\) is the number of distinct boundary components. Some numerical results are given.
scientific article; zbMATH DE number 220638