Application of parallel sparse direct methods in semiconductor device and process simulation

Abstract

We present PARDISO, a new scalable parallel sparse direct linear solver on shared memory multiprocessors. In this paper, we describe the parallel factorization algorithm which utilizes the supernode structure of the matrix to reduce the number of memory references with Level 3 BLAS. We also propose enhancements that significantly reduce the communication rate for pipelining parallelism. The result, is a greatly increased factorization performance. Furthermore, we have investigated popular shared memory multiprocessors and the most popular numerical algorithms commonly used for the solution of the classical drift-diffusion and the diffusion-reaction equations in semiconductor device and process simulation. The study includes a preconditioned iterative linear solver package and our parallel direct linear solver. Moreover, we have investigated the efficiency and the limits of our parallel approach. Results of several simulations of up to 300'000 unknowns for three-dimensional simulations are presented to illustrate our approach towards robust, parallel semiconductor device and process simulation.KeywordsFloat Point OperationElimination TreeShared Memory MultiprocessorNest DissectionSparse Direct SolverThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.