A Method for Solving an Exterior Boundary Value Problem for the Laplace Equation by Overlapping Domain Decomposition

We propose a numerical method for solving an exterior three-dimensional boundary value problem for the Laplace equation based on the overlapping decomposition of the computational domain. The initial boundary value problem is reduced to solving an operator equation for the sought values of the function on an auxiliary sphere enclosing the interior boundary. This equation is approximated by a system of linear algebraic equations which is solved by iterative methods in the Krylov subspaces. A series of numerical experiments for model problems with known solutions demonstrates not only the convergence of the method and the attained accuracy of the calculations but also a sufficiently short runtime.