Abstract:
A method for numerically solving the external Neumann problem is proposed based on new quadrature formulas for the simple layer potential constructed using analytical calculation of integrals. The method is tested on the Neumann problem for the Laplace equation outside of an ellipsoid, for which explicit solutions are found. It is shown that the numerical solution of the problem obtained by the proposed method uniformly approximates the exact solution and provides a lower error and faster convergence than the numerical solution obtained using standard quadrature formulas based on numerical integration. The dependence of the numerical solutions on the ellipsoid parameters are discussed.
