Partial Element Equivalent Circuit Based Parallel Electromagnetic Transient Simulation on GPU

The partial element equivalent circuit (PEEC) method effectively solves Maxwell’s equations in integral form by converting electromagnetic field components into the electrical circuit domain. This article proposes a novel transmission line modeling (TLM) based parallel PEEC time-domain solver to solve nonlinear electromagnetic problems. The method substitutes both linear and nonlinear components in the standard PEEC equivalent circuit with corresponding TLM models, leading to an electrical current-based linear network and a magnetic current-based nonlinear network. The proposed TLM-PEEC method effectively decouples the nonlinear elements from the linear network, enabling individual solutions for the nonlinearities and making it highly suitable for parallel processing. Each nonlinear element is solved using parallel Newton-Raphson (N-R) iterations, and the analytical calculation of the Jacobian is presented along with the algorithm. The parallelization of the TLM-PEEC method is explored and implemented on a many-core graphics processing unit (GPU) and a multi-core central processing unit (CPU) to provide detailed field-oriented information on electromagnetic transients in a single-phase 2-D shell-type transformer. The proposed architecture was easily coupled with an external network, and the accuracy and computational efficiency of the TLM-PEEC method were verified through similar simulation results obtained from Comsol Multiphysics.