Separable representations of the Poisson, Helmholtz and complex Helmholtz kernels

Abstract

For high accuracy applications of integral operators in higher dimensions the complexity of operation and storage usually grows exponentially with dimensions. One method that has proven successful for handling these difficulties are the separation of the integral kernels as linear combinations of products of one-dimensional kernels, commonly referred to as separation of variables. In this thesis we optimize the existing separable forms of the Poisson and complex Helmholtz kernels used in the program package MRCPP. We then find a new separable representation of the (non-complex) Helmholtz kernel.