Time Decomposition Method for the General Transient Simulation of Low-Frequency Electromagnetics

This paper describes a highly robust and efficient parallel computing method for the transient simulation of low-frequency electromagnetics with nonlinear materials and/or permanent magnets. In this method, time subdivisions are introduced to control the memory usage and nonlinear convergence. A direct block triangular matrix solver is applied to solve the formulated block matrix for each subdivision. This method has been implemented using the Message Passing Interface (MPI) for distributed memory parallel processing. Depending on the number of available MPI processes and physical memory, the entire nonlinear transient simulation can be divided into several subdivisions along the time-axis such that each MPI process handles only the computation for one time-step. Application examples are presented to demonstrate that this method can achieve excellent scalability of speedup.