Fast algorithm for the method of fundamental solution subjected to symmetry problems

The basic equations of a type of ellaptical PDEs and the coordinate transformation technique are provided in this paper. Based on the idea of image technique, the fundamental solutions are reconstructed for the symmetrical problems to reduce the computational cost. From the numerical experiments, it is seen that the results in this paper have good accuracy and high efficiency. MFS with coordinate transformation technique can solve more elliptical PDES compared with the classic field of harmonic and biharmonic equations. In particular, the programming, date preparing and the linear equations for computing can be greatly reduced by using the reconstructed fundamental solutions with image technique.