On an approximate solution of a class of boundary integral equations of the first kind
The paper proposes a collocation-like method for solving the first kind boundary integral equation associated with the Dirichlet problem for the Helmholtz equation in \(\mathbb R^3\). The method is based on the representation of the inverse of the single layer operator as the product of two inverses of second kind Fredholm integral operators and the corresponding hypersingular integral operator. Then an approximate solution can be obtained by applying a cubature of the hypersingular operator to the right hand side and the approximate solution of two Fredholm integral equations of the second kind. The author discusses cubature formulas for the double layer potential and the hypersingular integral on closed smooth surfaces, which leads to error estimates of the method.
scientific article; zbMATH DE number 6681164