A butterfly-accelerated volume integral equation solver for broad permittivity and large-scale electromagnetic analysis

• Main Authors: Sadeed Bin Sayed, Liu, Yang, Gomez, Luis J., Yucel, Abdulkadir C.
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2022
• Subjects: Engineering::Electrical and electronic engineering; Butterfly Algorithm; Direct Solver
• Online Access: https://hdl.handle.net/10356/163896
• Institution: Nanyang Technological University

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 $O(N\log^2N)$ construction cost of the HOD-BF-compressed system matrix and $O(N^{1.5}\log N)$ inversion cost for the preconditioner, where $N$ 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 $\mathcal{H}$ 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.