Efficient Marching-on-in-Degree Solver of Time Domain Integral Equation with Adaptive Cross Approximation Algorithm-Singular Value Decomposition
Efficient Marching-on-in-Degree Solver of Time Domain Integral Equation with Adaptive Cross Approximation Algorithm-Singular Value Decomposition
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发表时间：
2012
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通讯作者：
Huan-huan Zhang;Quanquan Wang;Yifei Shi;Ru-Shan Chen
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作者：
Huan-huan Zhang;Quanquan Wang;Yifei Shi;Ru-Shan Chen
将奇异值分解后压缩的自适应交叉逼近算法（ACA-SVD）引入时域积分方程的逐阶求解中，分析了理想导体（PEC）的瞬态电磁散射。基于八叉树对计算域进行多级分组。利用ACA-SVD算法计算各层上的阻抗矩阵。而由自身和相邻基团形成的阻抗矩阵完全是用传统的方法计算的。数值结果表明，所提出的方法可以大大减少内存需求和矩阵向量积（MVP）的时间，每次迭代。指标项─时域积分方程、入度步进、瞬态散射、自适应交叉逼近算法、奇异值分解。
─ Adaptive cross approximation algorithm with singular value decomposition postcompression (ACA-SVD) is introduced into the marching-on-in-degree solver of time domain integral equation for the analysis of transient electromagnetic scattering from perfect electric conductor (PEC). The computational domain is divided into multilevel groups based on octree. ACA-SVD algorithm is utilized to compute the impedance matrices associated with the wellseparated groups at each level. Whereas, the impedance matrices formed by self and neighboring groups are calculated entirely in the traditional manner. Numerical results demonstrate that the proposed method can greatly reduce the memory requirement and matrix-vector product (MVP) time per iteration. Index Terms ─ Time domain integral equation, marching-on-in-degree, transient scattering, adaptive cross approximation algorithm, singular value decomposition.