Finite-difference DC electrical field modeling on 2D and 2. 5D undulate topography

Undulate surface DC field numerical simulation using finite element method is commonly used, mainly because of its flexible curved boundary treatment capacity. However, finite element is more complex than the finite difference. If we allow the finite difference to have also similar ability to deal with the curved boundary, that simulation will become easy. In this paper, non-equidistant difference is used at non-regular interior points and the boundary conditions are directly implemented to the undulate surface points, which overcomes the drawback of transfer method to change the shape of the surface, making finite-difference based on the Cartesian grid have a strong ability to deal with the boundary. Through the comparison of numerical and analytical solutions of the level surface in two-dimension and 2. 5 dimension, as well as the two-dimensional numerical solution for undulate surface and the solution of conformal mapping theory, it is shown that the method is effective. Finally, we give some numerical examples.