H-Matrix Arithmetic for Fast Direct and Iterative Method of Moment Solution of Surface-Volume-Surface EFIE for 3-D Radiation Problems
H-Matrix Arithmetic for Fast Direct and Iterative Method of Moment Solution of Surface-Volume-Surface EFIE for 3-D Radiation Problems
复制标题
3-D 辐射问题表面-体积-表面 EFIE 矩解快速直接迭代法的 H 矩阵算法
DOI：
10.2528/pierb18101901
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发表时间：
2018
影响因子：
--
通讯作者：
V. Okhmatovski
中科院分区：
文献类型：
--
作者：
R. Gholami;Jamiu B. Mojolagbe;A. Menshov;F. S. H. Lori;V. Okhmatovski
提出了一种基于分层(H-)矩阵的加速求解均匀介质目标散射和辐射问题的表面-体积-表面电场积分方程(SVS-EFIE)的矩量法(MoM)的快速算法。由于SVS-EFIE具有将散射体表面的切向等效电流映射为体极化电流的积分算子和将体极化电流映射为散射电场的切向分量的积分算子的乘积，其MoM离散化产生非方阵的乘积。描述了MOM离散化积分算子的非平方H-矩阵的构造。给出了与非平方H-矩阵乘积有关的算法。详细分析了H-矩阵运算所需的内存和CPU时间复杂度，并进行了数值验证。对于生物电磁学应用中的低损耗电介质物体和高损耗生物组织，对所提出的算法进行了数值验证。数值实验表明，与näıve MoM方法相比，该方法显著减少了内存使用量，提高了计算速度，从而解决了大规模散射和辐射问题。
Hierarchical (H-) matrix based fast direct and iterative algorithms are presented for acceleration of the Method of Moment (MoM) solution of the Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE) formulated for scattering and radiation problems on homogeneous dielectric objects. As the SVS-EFIE features the product of the integral operator mapping the tangential equivalent electric current on the surface of the scatterer to the volume polarization current and the integral operator mapping the volume polarization current to the tangential component of the scattered electric field, its MoM discretization produces the product of non-square matrices. Formation of the non-square H-matrices for the MoM discretized integral operators is described. The algorithms for arithmetics pertinent to the product of the non-square H-matrices are explained. The memory and CPU time complexity scaling of the required H-matrix operations are analyzed in details and verified numerically. The numerical validation of the proposed algorithm is provided for both the lowloss dielectric objects as well as for the high-loss biological tissues found in the bioelectromagnetics applications. The numerical experiments demonstrate a significant reduction of memory usage and a considerable speedup for CPU time compared to näıve MoM, thus, enabling solution of the large-scale scattering and radiation problems with the SVS-EFIE.