A Multigrid Approach to Solving Poisson's Equation for a p-n Diode

The solution of the Poisson equation, using the finite element method, offers a multi­ tude of decisions regarding the solution procedure. Factors which will influence these decisions include both the ease of implementatio n and the computer time required, Multigrid is an approach to the solution method. In this paper, the use of multigrid with the very straightforward Jacobi relaxation is described. Alone, Jacobi relaxation is slow to converge. However, problems associated with it are addressed by multigrid, and a neat and useful algorithm results. It this paper, the ideas of multigrid are summarised. These ideas are extended to cover the use of linear interpolation with the non-linear Poisson equation. The paper concludes with a two-dimensiona l example, illustrating the algorithms developed,