Domain decomposition technique for the continuity equations of semiconductor device models

摘要

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 used. This kind of preconditioner is suitable for parallel computing and efficient for the linear system with rapidly varied solutions. Since the class of the linear system we considered is a special kind of an unsymmetric matrix we modify the PCG to this case as well. With our modified PCG method, we compare the preconditioner which is constructed by using Incomplete Cholesky decomposition without fill-in preconditioner to our preconditioners which are based on the domain decomposition technique. We find that the latter is much more efficient than the former for our semiconductor model problem.