The method of approximate particular solutions for solving anisotropic elliptic problems

In this paper, we study the method of approximate particular solutions for solving anisotropic elliptic-type problems. A special norm associated with the anisotropic differential operator is introduced for the design of anisotropic radial basis functions. Particular solutions of anisotropic radial basis function can be found by the same procedure as that of regular radial basis functions under Laplace operator. Consequently, the method of approximate particular solutions can be extended to anisotropic elliptic-type problems. Numerical results are presented for a number of two-dimensional anisotropic diffusion problems. It shows that this method permits the choice of collocation points independent of the magnitude of anisotropy.