2025 University Circle Las Vegas, Nevada 89119 USA
Department of Mathematical Sciences University of Nevada at Las Vegas Las Vegas, Nevada 89154 USA
Abstract:
We have shown how to couple a numerical method due to Atkinson for computing particular solutions to a class of elliptic differential equations with a variety of boundary element methods, which alleviates the problem of domain discretization for solving inhomogeneous equations. When the inhomogeneous term is of the form typically used in the dual reciprocity method, Atkinson's formula is such that only boundary integrals need to be approximated numerically. If this method is coupled with the method of potentials, it results in a computational technique which requires neither boundary nor domain discretization. Some numerical results are given validating our approach.