This paper examines the application of the multigrid method to the steady state semiconductor equations in one dimension. A number of attempts reported in the literature have yielded only limited success in applying multigrid algorithms to this sensitive problem, suggesting that a more careful look in relatively simple circumstances is worthwhile. \nSeveral modifications to the basic multigrid algorithm are evaluated based on their performance for a one-dimensional model problem. It was found that use of a symmetric Gauss-Seidel relaxation scheme, a special prolongation based on using the difference operator, and local relaxation sweeps near junctions, produced a robust and efficient code. This modified algorithm is also successful for a wide variety of cases, and its performance compares favourably with other multigrid algorithms that have been applied to the semiconductor equations.
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