超松弛迭代-双共轭梯度在三维电磁问题有限元分析中的应用

Application of SSOR Preconditioned BICG Method to the Analysis of 3-D Electromagnetic-Field Boundary Value Problems Based On Vector FEM

应用矢量有限元方法(FEM)对三维电磁问题进行分析,研究应用超松弛迭代(SSOR)方法预处理的双共轭梯度(BICG)求解有限元线性方程组的收敛特性.文中给出了SSOR-BICG方法的高效算法,并对三维腔体的电磁散射问题和三维波导不连续性结构进行了分析.研究表明,通过SSOR预处理,在不增加内存消耗的情况下,有限元系数矩阵性态大为改善,BICG求解速度大大提高.SSOR-BICG方法在计算时间上比BICG方法和共轭梯度法(CG)分别可以提高了4倍和44倍,从而为电大目标的有限元方法快速分析提供技术支持.

Vector finite-element method （FEM） is applied for the analysis of 3-D electromagnetic field boundary value problems, then, the application of symmetric successive overrelaxation （SSOR） preconditioned Biconjugate- gradient （BICG） method is investigated for solving the resulting linear equations. The efficient SSOR-BICG implementation is presented for complex coefficient matrix. The matrix condition is improved evidently with the preconditioning matrix that is structured with no additional computational time and storage. The SSOR-BICG can reach convergence nearly 4 times faster and 44 times faster than that of BICG and conjugategradient （CG） respectively in CPU time for some typical structures. The presented numerical results demonstrate that, when vector FEM is employed to analyze 3-D electromagnetic-field problems, the SSOR-BICG method is efficient for solving the resulting large-scale FEM equations.