Compressing H2 Matrices for Translationally Invariant Kernels

H2 matrices provide compressed representations of the matrices obtained when discretizing surface and volume integral equations. The memory costs associated with storing H2 matrices for static and low-frequency applications are O(N). However, when the H2 representation is constructed using sparse sa...

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Bibliographic Details
Published in:Applied Computational Electromagnetics Society journal 2020-01, Vol.35 (11), p.1392
Main Authors: Adams, R J, Young, J C, Gedney, S D
Format: Article
Language:English
Subjects:
Computer engineering
Integral equations
Invariants
Representations
Volume integral equations
Online Access:Get full text
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Summary:H2 matrices provide compressed representations of the matrices obtained when discretizing surface and volume integral equations. The memory costs associated with storing H2 matrices for static and low-frequency applications are O(N). However, when the H2 representation is constructed using sparse samples of the underlying matrix, the translation matrices in the H2 representation do not preserve any translational invariance present in the underlying kernel. In some cases, this can result in an H2 representation with relatively large memory requirements. This paper outlines a method to compress an existing H2 matrix by constructing a translationally invariant H2 matrix from it. Numerical examples demonstrate that the resulting representation can provide significant memory savings.
ISSN:1054-4887
1943-5711