Implementation of sparta, a Highly Parallel Circuit Simulator by the Preconditioned Jacobi Method, on a Distributed Memory Machine

This paper investigates an efficient implementation of circuit simulator sparta based on the preconditioned Jacobi method on a loosely coupled distributed memory machine Fujitsu AP1000. The preconditioned relaxation methods are linear solvers effective in large scale circuit simulations. Because the preconditioned Jacobi method has a high parallelism, the only problem of parallelization of sparta is the application of the preconditioner to the residual vector. This paper investigates the matrix mapping schemes and the communication methods for efficient preconditioner application. The peculiarity of the preconditioner in sparta is a few full rows and columns, in spite of its rather high sparsity. The column-row mapping is the best scheme by far, where the decisive point is the low communication requirements. The best communication method is the far-first cascade method, despite the out-of-order reception of messages of the one-to-one method. The parallel efficiency of sparta is reporte..