Institute for Numerical and Computational Analysis Dublin, Ireland A Domain Decomposition Preconditioner for the Continuity Equation of the Semiconductor Problem

In this paper, we use the PCG method to solve the linear systems obtained from the continuity equations of semiconductor models. A new kind of preconditioner which is based on the domain decomposition technique is discussed in detail. This kind of preconditioner is suitable for parallel computing and efficient for the linear system with rapidly varied solutions. Since the class of linear systems we considered is a special kind of nonsymmetric matrix we modify the PCG to this case as well. With our modified PCG, we compare the preconditioner IC(0), which is an Incomplete Cholesky decomposition without fill-in, to our preconditioners which are on the domain decomposition technique. We find that the latter is much more efficient than the former for our semiconductor model problem.