In this paper, a solver based on a 3D boundary element method (BEM) is presented and verified on a transformer geometry. Using a triangular surface mesh of a winding, the unknown charge distribution is found from known potentials of surfaces using the integral equation approach and point matching. The capacitance matrix is calculated from known potentials in nodes of the system. The application of BEM and point‐matching results in a fully populated system matrix. Therefore, a matrix reduction technique adaptive cross approximation (ACA) is employed in order to reduce the CPU time and memory requirements. Both the accuracy of the direct and the accuracy of the ACA approach are benchmarked against the results obtained using the professional finite element method (FEM)‐based software.

中文翻译：

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使用3D边界元法和自适应交叉近似的变压器电容矩阵计算

本文提出了一种基于3D边界元方法（BEM）的求解器，并在变压器几何上进行了验证。使用绕组的三角形表面网格，使用积分方程方法和点匹配从已知的表面电势中找到未知的电荷分布。电容矩阵是根据系统节点中的已知电势计算的。BEM和点匹配的应用导致了一个完全填充的系统矩阵。因此，为了减少CPU时间和内存需求，采用了矩阵约简技术自适应交叉逼近（ACA）。直接精度和ACA方法的精度均以使用基于专业有限元方法（FEM）的软件获得的结果为基准。