A Butterfly-Accelerated Volume Integral Equation Solver for Broad Permittivity and Large-Scale Electromagnetic Analysis

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...

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Bibliographic Details
Published in:IEEE transactions on antennas and propagation 2022-05, Vol.70 (5), p.3549-3559
Main Authors: Sayed, Sadeed Bin, Liu, Yang, Gomez, Luis J., Yucel, Abdulkadir C.
Format: Article
Language:English
Subjects:
Butterfly algorithm
Complexity theory
Computing time
Construction costs
Cost analysis
direct solver
ENGINEERING
fast solver
Formulas (mathematics)
Integral equations
Interpolation
Linear systems
Matrix decomposition
Memory management
Permittivity
preconditioners
Scattering
Solvers
volume integral equation
volume integral equation (VIE)
Volume integral equations
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Description
Summary: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 ^{2}N) 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.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2021.3137193