Analytical regularization for diffraction problem: Open shell of revolution

Abstract

A rigorous and numerically efficient approach for solving the scalar diffraction problem for open arbitrarily shaped shell of revolution is developed, when Dirichletpsilas boundary condition is imposed. The approach is based on the analytical regularization method. Seeking the solution by its integral representation, we determine the singular features of the kernel, and decompose it into the singular canonical part, and a regular remainder. Then, utilizing an appropriate technique, the problem is equivalently reduced to integral equation of the first kind, and then - to an infinite system of linear algebraic equations of the second kind. The last is well conditioned always, and its solution can be efficiently obtained to any pre-specified accuracy.