Many simulators in several fields use the finite difference method and they must solve the large sparse linear equations related. Particularly, if we use the direct solution method because of the convergency problem, it is necessary to adopt a method that can reduce the CPU time greatly. The Multi-Step Diakoptics (MSD) method is proposed as a parallel computation method with a direct solution which is based on Diakoptics, that is, a tearing-based parallel computation method for the sparse linear equations. We have applied the MSD algorithm for one, two and three dimensional finite difference methods. We require a parallel schedule that automatically partitions the desired object's region for study, assigns the processor elements to the partitioned regions according to the MSD method, and controls communications among the processor elements. This paper describes a parallel scheduling that was extended from a one dimensional case to a three dimensional case for the MSD method, and the evaluation of the algorithm using a massively parallel computer with distribuled memory(AP1000).

For the development of a practical device simulation, it is necessary to solve the large sparse linear equations with a high speed computation of direct solution method. The use of parallel computation methods to solve the linear equations can reduce the CPU time greatly. The Multi Step Diakoptics (MSD) algorithm, is proposed as one of these parallel computation methods with direct solution, which is based on Diakoptics, that is, a tearing-based parallel computation method for sparse linear equations. We have applied the MSD algorithm to device simulation. This letter describes the partition and connection schedules in the MSD algorithm. The evaluation of this algorithm is done using a massively parallel computer with distributed memory (AP1000).