Fast O(N log N) Algorithm for Generating Rank-Minimized H2-Representation of Electrically Large Volume Integral Equations

In this article, we propose a fast algorithm to generate a rank-minimized \mathcal {H}^{2} -representation for solving electrically large volume integral equations (VIEs). Unlike existing methods whose complexity is as high as quadratic, the proposed algorithm has linearithmic complexity, and thus,...

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Bibliographic Details
Published in:IEEE transactions on antennas and propagation 2022, Vol.70 (8), p.6944-6956
Main Authors: Wang, Yifan, Jiao, Dan
Format: Article
Language:English
Subjects:
Algorithms
Approximation algorithms
Clustering algorithms
Complexity
Computational complexity
Cubes
electrically large analysis
fast solvers
H2 matrix
Indexes
Integral equations
Mathematical analysis
matrix compression
Matrix converters
Nonhomogeneous media
rank-minimized compression
Representations
Volume integral equations
volume integral equations (VIEs)
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Summary:In this article, we propose a fast algorithm to generate a rank-minimized \mathcal {H}^{2} -representation for solving electrically large volume integral equations (VIEs). Unlike existing methods whose complexity is as high as quadratic, the proposed algorithm has linearithmic complexity, and thus, it can handle problems with large electrical sizes. Furthermore, the algorithm is purely algebraic and kernel independent. Numerical experiments on electrically large 3-D arrays of dielectric cubes having over 33 million unknowns demonstrate the efficiency and accuracy of the proposed algorithm.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2022.3168749