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%.

中文翻译：

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用于带场电路耦合的大规模并行 3-D 有限元仿真的无矩阵边缘域分解方法

在本文中，提出了一种新的边缘域分解 (EDD) 方法来解决电磁设备和瞬态场电路协同仿真的 3-D 非线性有限元 (FE) 问题。该方法应用简化的磁矢量势公式来离散基于 3-D 边缘元素的物理问题，并将求解区域划分为许多子域，其中仅包含一个未知边缘。轻量级非线性子域系统的解决方案可以大规模并行化，邻居到邻居的通信方案消除了组装全局有限元矩阵的需要。本文还介绍了一种处理大涡流的间接耦合方案，以将 EDD FE 系统与外部电路连接起来。然后在多核 GPU 上实现上述算法以进行瞬态场电路协同仿真。结果显示了自动测量特性，与商业 FE 软件的比较表明加速超过 43 倍，相对误差小于 2%。