Diffraction from Arbitrarily Shaped Open Shells of Revolution: Static Case

A mathematically rigorous and numerically efficient approach is developed for solving the Laplace equation with Dirichlet boundary condition on a closed or open arbitrary shaped surface of revolution. Although important in itself, the problem also provides a first step towards the solution of the related wave scattering problem. The generalized method of analytical regularization transforms the problem to a well-conditioned infinite system of linear algebraic equations of the second kind. This provides a robust numerical solution with any desired accuracy.