求解电磁场边值问题有限元线性系统的新型预条件算法

摘要

针对矢量有限元分析三维电磁问题得到的大型复对称且高度非正定的线性系统的求解，提出了一种新型预条件算法N-AINV，其构造是基于复偏移Laplace算子结合带主元补偿的AINV稀疏近似逆算法，该算法能改善系数矩阵特征谱并避免主元崩溃。数值结果表明，提出的新型预条件算法能获得比其它常规预条件法更稳定的求解，并同时有效提高求解效率，缩短仿真用时。%A new preconditioning technique for solving large linear systems arising from edge-based finite element method (FEM) analysis of three-dimensional (3-D) electromagnetic problems is presented. This method is achieved by applying a shift-ed-Laplace operator scheme and sparse approximate inverse to symmetric linear BCG (LBCG). The main purpose is to generate a more robust and efficient preconditioner. Numerical results on several electromagnetic problems show that, by comparing with other conventional preconditioning techniques, this technique is more efficient and robust, and can greatly reduce the simulation time.