Matrix-Free Edge-Domain Decomposition Method for Massively Parallel 3-D Finite Element Simulation With Field-Circuit Coupling

Abstract

In this article, a novel edge-domain decomposition (EDD) method is proposed to solve 3-D nonlinear finite element (FE) problems of electromagnetic devices and transient field circuit co-simulation. The method applies reduced magnetic vector potential formulation to discretize the physical problem based on 3-D edge elements, and the solution region is divided into many sub-domains that only contain one edge unknown. The solution of lightweight nonlinear sub-domain systems can be massively parallelized, and the neighbor-to-neighbor communication scheme eliminates the need to assemble the global FE matrix. This article also introduces an indirect coupling scheme to handle large eddy currents to interface the EDD FE system with external circuits. The abovementioned algorithms are then implemented on a many-core GPU for transient field circuit co-simulation. The result shows an auto-gauging property, and the comparison with a commercial FE software indicates a speedup of over 43 times with relative error less than 2%.Index Terms-3-D edge element, domain decomposition, Eddy current field, field-circuit coupling, finite element (FE) method, graphics processors, nonlinear, parallel processing, reduced magnetic vector potential.

Model Order Reduction for Real-Time FPGA-Based Finite Element Transient Simulation of Three-Phase Transformer

“…This method separately considers the FE model equations and the external circuit equations. It is a common method which has been used in many papers such as [34] and can ensure the enough accuracy of the results. In this paper, the low-order model is used to realize the indirect coupling method.…”

Time-Stepped Finite-Element Modeling of Three-Phase Transformer for Electromagnetic Transient Emulation on FPGA

“…On the contrary, the indirect coupling methods solve the circuit and the FE model individually. One indirect coupling method proposed in [24] which can guarantee accurate results even under a strong eddy current is adopted in this work.…”

“…However, each entry in V coil is the function of all six currents through the coils due to the energy exchange by the transformer between the electric field and the magnetic field. Based on the aforementioned relationship between the EMF and the current, the Jacobian matrix can be calculated by solving the same FEM equation as ( 5) with different excitation current vector on the right-hand side and making a weighted sum with (9) as explained in [24]. With (9) and the determined relationship between the EMF and the current, these six coupled equations can be solved by Newton-Raphson method after two to four iterations [24].…”

“…Based on the aforementioned relationship between the EMF and the current, the Jacobian matrix can be calculated by solving the same FEM equation as ( 5) with different excitation current vector on the right-hand side and making a weighted sum with (9) as explained in [24]. With (9) and the determined relationship between the EMF and the current, these six coupled equations can be solved by Newton-Raphson method after two to four iterations [24]. Even though the number of iterations for the field-circuit coupling is not large, the involved computation workload at each iteration is quite heavy.…”