Compressing H2 Matrices for Translationally Invariant Kernels

Authors

  • R. J. Adams Electrical & Computer Engineering University of Kentucky Lexington, KY, USA
  • J. C. Young Electrical & Computer Engineering University of Kentucky Lexington, KY, USA
  • S. D. Gedney Electrical Engineering University of Colorado Denver Denver, CO, USA

Keywords:

integral equations, sparse matrices

Abstract

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.

References

S. Börm, "Construction of data-sparse H2-matrices by hierarchical compression," SIAM Journal on Scientific Computing, vol. 31, no. 3, pp. 1820-1839, 2009.

W. Hackbusch, Hierarchical Matrices: Algorithms and Analysis (Springer Series in Computational Mathematics). Berlin: Springer-Verlag, 2015.

X. Xu and R. J. Adams, "Sparse matrix factorization using overlapped localizing LOGOS modes on a shifted grid," IEEE Transactions on Antennas and Propagation, vol. 60, no. 3, pp. 1414-1424, 2012.

J. C. Young and S. D. Gedney, "A Locally Corrected Nystrom Formulation for the Magnetostatic Volume Integral Equation," IEEE Transactions on Magnetics, vol. 47, no. 9, pp. 2163-2170, Sep. 2011.

Downloads

Published

2020-11-07

How to Cite

R. J. Adams, J. C. Young, & S. D. Gedney. (2020). Compressing H2 Matrices for Translationally Invariant Kernels. The Applied Computational Electromagnetics Society Journal (ACES), 35(11), 1392–1393. Retrieved from https://journals.riverpublishers.com/index.php/ACES/article/view/7595

Issue

Section

Articles