Solution of Volume-Surface Integral Equation Accelerated by MLFMA and Skeletonization

A fast algorithm for solving large multi-scale scattering problems by the volume-surface integral equation (VSIE) is proposed. The sub-matrices of the near-field interactions (NFIs) in terms of the multi-level fast multipole algorithm (MLFMA) are compressed by the skeletonization after the theoretic...

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Bibliographic Details
Published inIEEE transactions on antennas and propagation Vol. 70; no. 7; pp. 6078 - 6083
Main Authors Liu, Yan-Nan, Pan, Xiao-Min
Format Journal Article
LanguageEnglish
Published New York IEEE 01.07.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Algorithms
Impedance
Impedance matrix
Integral equations
Method of moments
Multi-level fast multipole algorithm (MLFMA)
Multipoles
preconditioner
Scattering
Skeleton
skeletonization
Sparse matrices
Surface treatment
Testing
volume–surface integral equations (VSIEs)
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Summary:A fast algorithm for solving large multi-scale scattering problems by the volume-surface integral equation (VSIE) is proposed. The sub-matrices of the near-field interactions (NFIs) in terms of the multi-level fast multipole algorithm (MLFMA) are compressed by the skeletonization after the theoretical and numerical investigations on their low-rankness are carried out. A block-diagonal preconditioner (BDP) based on the recursive skeletonization (RS) is developed to improve the conditioning of the impedance matrix of the VSIE. The rules to select hyperparameters in the proposed method are given. Numerical experiments conducted on scattering problems show the performance of the proposed algorithm.
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2022.3140502