Multigrid Applied to Two-Dimensional Exponential Fitting for Drift-Diffusion Models

摘要

The author considers drift-diffusion models. An important application of these equations is in the field of semiconductor device simulation. It is well-known that multigrid methods can be very efficient for solving the large sparse systems which result from the discretization of elliptic boundary value problems. In the situation here there is no 'standard' multigrid method which can be used. In another paper, the author introduced a multigrid method for the discretized problem if c identically = 0. This method is based on a connection between the discretization resulting from the 2D exponential fitting method and a suitable nonconforming linear finite element discretization. In the paper it is shown that such a connection also exists for the situation c not identically = 0 (in which the exponential fitting method is essentially different compared with c identically = 0). This then leads to a reasonable multigrid method. The author describes the resulting algorithm and presents some numerical results.