Parallelization of EMAP3D based on element-by-element Jacobi preconditioned conjugate gradient method

Abstract

The demand for more accurate analyses of electromechanical systems, such as electromagnetic launchers and pulsed rotating power supplies, requires an increase in the size of the finite-element model of these systems. It is not uncommon for the number of unknowns for such a model to reach a half million. A parallel computing system with multiple processors and distributed memory, such as a PC cluster, makes it possible to obtain solutions for large-scale problems in reasonable times. In order to utilize this parallel hardware architecture, the software needs to be parallelized accordingly. Electromechanical Analysis Program in Three Dimensions (EMAP3D) is parallelized based on the element-by-element Jacobi preconditioned conjugate gradient (EBEJPCG) method because it is easily adopted into a parallel scheme and has low memory requirements because the formation of the global matrix is not necessary. The details of this algorithm are described in this paper. A block armature railgun was used to investigate this parallel algorithm on the Institute for Advanced Technology's (IAT's) eight-node PC-based Beowulf cluster. The performance of the algorithm in terms of speed-up ratio is presented.