Inverse solution for poisson equations using drm boundary element models—identification of space charge distribution

Abstract

There is a kind of problem in which we like to identify the source such as the electric space charge or force distribution in a domain, from the remotely observed data such as electric potential or force and flux or displacement distribution observed over the boundary. This corresponds to solving the Poisson problems inversely. For the solution procedure, the boundary element method is advantageous as numerical integration can be made only over the boundary for Laplace problems but the advantage fails for Poisson problems. The Dual Reciprocity Method (DRM) provides a technique for taking the domain integrals associated with the inhomogeneous term to the boundary. In this paper the identification of unknown electric charge distribution is considered using DRM, with which the inhomogeneous term can equivalently be expressed as the linear combination of the functions associated with the particular solutions. Numerical examples are presented to demonstrate the availability of the approach. First we consider t...