Numerical solution of 3-D Neuman problem for scalar Helmholtz equation at the bodies of complex shapes

Abstract

Our paper is concerned with solving the 3D outside boundary Neuman problem for the scalar Helmholtz equation. By means of the double layer potential, this problem reduces to the hypersingular integral equation of the 1-st kind. The numerical method for solving the hypersingular integral equation at bodies of arbitrary form is proposed. This method is a method of discrete vortex type. Comparison of the exact solution for a sphere with the numerical one is carried out. Results of the computation for a cube and for a plate are presented.