A reliable estimation method of a dipole for three-dimensional Poisson equation

We discuss an inverse source problem for three-dimensional Poisson equation. The source term is expressed as a dipole that consists of two contiguous point sources. Our problem is estimating the dipole moment and its location under the condition that the potential and flux can be observed on the boundary. We propose a numerical method based on a weighted residual approach, which need not use direct analysis for the governing equation. The method should be reliable since the error caused by the numerical integration and observation noise can be evaluated theoretically. The effectiveness of the method is shown by numerical examples.