Sayed Sadeed B, Liu Yang, Gomez Luis J, Yucel Abdulkadir C
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798.
Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
IEEE Trans Antennas Propag. 2022 May;70(5):3549-3559. doi: 10.1109/tap.2021.3137193. Epub 2021 Dec 28.
A butterfly-accelerated volume integral equation (VIE) solver is proposed for fast and accurate electromagnetic (EM) analysis of scattering from heterogeneous objects. The proposed solver leverages the hierarchical off-diagonal butterfly (HOD-BF) scheme to construct the system matrix and obtain its approximate inverse, used as a preconditioner. Complexity analysis and numerical experiments validate the construction cost of the HOD-BF-compressed system matrix and inversion cost for the preconditioner, where is the number of unknowns in the high-frequency EM scattering problem. For many practical scenarios, the proposed VIE solver requires less memory and computational time to construct the system matrix and obtain its approximate inverse compared to a matrix-accelerated VIE solver. The accuracy and efficiency of the proposed solver have been demonstrated via its application to the EM analysis of large-scale canonical and real-world structures comprising of broad permittivity values and involving millions of unknowns.
提出了一种蝶形加速体积积分方程（VIE）求解器，用于对异质物体的散射进行快速准确的电磁（EM）分析。所提出的求解器利用分层非对角蝶形（HOD-BF）方案来构建系统矩阵并获得其近似逆矩阵，用作预处理器。复杂度分析和数值实验验证了HOD-BF压缩系统矩阵的构建成本以及预处理器的求逆成本，其中 是高频电磁散射问题中的未知数数量。对于许多实际场景，与矩阵加速VIE求解器相比，所提出的VIE求解器在构建系统矩阵和获得其近似逆矩阵时需要更少的内存和计算时间。通过将其应用于包含广泛介电常数且涉及数百万未知数的大规模典型结构和实际结构的电磁分析，证明了所提出求解器的准确性和效率。
