Inverse problem - determining unknown distribution of charge density using the dual reciprocity method

摘要

Presents the use of the dual reciprocity method (DRM) for solving inverse problems described by Poisson's equation. DRM provides a technique for taking the domain integrals associated with the inhomogeneous term to the boundary. For that reason, the DRM is supposed to be ideal for solving inverse problems. Solving inverse problems, a linear system is produced which is usually predetermined and ill-posed. To solve that kind of problem, implements the Tikhonov algorithm and compares it with the analytical solution. In the end, tests the whole algorithm on different problems with analytical solutions.