Concentrators with arbitrary geometries are designed based on the numerical solution of Laplace's equation, with which the material parameters can be independently obtained without any knowledge of the corresponding coordinate transformation. Results show that the concentrator designed using the numerical method has the same scattering and concentrating properties as that designed using the analytical method, except for a slight difference in the stretching region, which, however does not influence the design of the concentrator. The method developed in this paper is general and flexible for designing arbitrary concentrators. The validity of such a method and the concentrating effects are confirmed by full-wave simulations.