ON THE NUMERICAL SOLUTION OF THE THREE-DIMENSIONAL NEUMANN PROBLEM FOR THE HELMHOLTZ EQUATION BY THE POTENTIAL METHOD

The three-dimensional exterior Neumann problem for the Helmholtz equation is considered. Using the potential method, it is reduced to a boundary weakly singular Fredholm integral equation of the second kind, which is solved numerically. The accuracy is increased and the computational complexity of the numerical solution algorithm is reduced by averaging the kernel of the integral operator and localizing its singular part during discretization using simple analytical expressions. Examples of using this approach in the numerical solution of the original problem are given.