棱边元分区的区域分解算法及其在电磁问题中的应用

针对三维电磁问题，该文提出了采用非结构化网格剖分计算区域，并按单元进行区域划分的区域分解算法。将原求解区域划分为若干个不重叠的子区域，先通过求解容量矩阵获得子区域之间连接边界上的场值，再利用矢量有限元快速计算出每个子区域内部的场值，显著地降低了计算复杂度和存储量。通过引入预条件的Krylov子空间法求解容量矩阵方程，加速了收敛，进一步提高了效率。数值算例验证了该方法的准确性和有效性。

Edge-Element Partitioning Domain Decomposition Method for Electromagnetic Problems

A fast domain decomposition method is presented for the solution of electromagnetic problems arising in three-dimensions. The original computation domain is meshed and decomposed into several nonoverlapping subdomains by edge-element partitioning technique, which yields a capacitance matrix. Once the unknowns on the interfaces between subdomains have been obtained through the capacitance matrix, the interior unknown fields in each subdomain can be computed with vector finite element method in parallel. Compared with the conventional numerical methods, such as finite element method, method of moments, the present method can greatly reduce the computational complexity and the storage requirement. A preconditioned Krylov subspace method is also developed to accelerate the convergence of the capacitance matrix, and improve the efficiency further. The validity and computational efficiency have been verified by numerical examples.