基于相位提取基函数的高效区域分解方法

为了进一步提高电大导体目标电磁散射问题的计算能力，给出了一种高效的区域分解方法。该方法采用定义在曲面三角形单元上的相位提取基函数来展开目标表面的感应电流，大幅减少了待求未知量的数目；同时结合区域分解方法，将原问题分解为若干个重叠的子问题并逐个进行求解，进一步降低了峰值内存需求。此外，为了简化缓冲区的构造过程，采用了仅一层锯齿状的边长约为0.5个波长的三角形单元作为缓冲区，取得了良好的收敛效果。多层快速多极子方法被用于加速矩矢相乘运算。数值算例说明了该方法的高效性和稳健性。

An Efficient Domain Decomposition Method Using Phase Extracted Basis Functions

To further improve the ability of analyzing electromagnetic scattering from electrically large perfect electric conducting objects, an efficient domain decomposition method is presented. In this method, the approximated current density is expanded with the phase-extracted basis functions defined over curvilinear triangular patches, and the number of unknowns to be solved is significantly reduced. Meanwhile, to further reduce the memory requirement, the original problem domain is divided into a number of small overlapped sub-domains and the sub-domain problems are solved one by one. In addition, the buffer regions introduced in this method are limited to only a single layer of jagged triangular mesh cells whose edges are about half a wavelength long, leading to a simplified construction process of buffer zones as well as a smaller number of additional variables to be solved. A good convergence behavior is observed. The multilevel fast multipole algorithm is applied to accelerate the matrix-vector products. Numerical examples are given to show the efficiency and robustness of the proposed approach.