Fast Multilevel Computation of Low-Rank Representation of ℋ-Matrix Blocks

Yaniv Brick; Ali E. Yilmaz

doi:10.1109/TAP.2016.2617376

Fast Multilevel Computation of Low-Rank Representation of ℋ-Matrix Blocks

Yaniv Brick, Ali E. Yilmaz

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

Abstract

A physics-based algorithm for accelerating the computation of method of moments matrix blocks' low-rank approximation is presented. The algorithm relies on efficient sampling of phase- and amplitude-compensated interactions using nonuniform grids. Rank-revealing analysis is applied, in a multilevel fashion, to matrices of reduced column and row dimensions that describe subdomains' interactions with these coarse grids, rather than to the original matrix blocks. As a result, significant savings are achieved, especially for the inherently more compressible dynamic quasi-planar and quasi-static cases. The algorithm's reduced storage and computation time requirements are estimated analytically and verified numerically for representative examples.

Original language	English
Article number	7590029
Pages (from-to)	5326-5334
Number of pages	9
Journal	IEEE Transactions on Antennas and Propagation
Volume	64
Issue number	12
DOIs	https://doi.org/10.1109/TAP.2016.2617376
State	Published - 1 Dec 2016
Externally published	Yes

Keywords

Compression algorithm
integral equations
moment methods

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/TAP.2016.2617376

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title = "Fast Multilevel Computation of Low-Rank Representation of ℋ-Matrix Blocks",

abstract = "A physics-based algorithm for accelerating the computation of method of moments matrix blocks' low-rank approximation is presented. The algorithm relies on efficient sampling of phase- and amplitude-compensated interactions using nonuniform grids. Rank-revealing analysis is applied, in a multilevel fashion, to matrices of reduced column and row dimensions that describe subdomains' interactions with these coarse grids, rather than to the original matrix blocks. As a result, significant savings are achieved, especially for the inherently more compressible dynamic quasi-planar and quasi-static cases. The algorithm's reduced storage and computation time requirements are estimated analytically and verified numerically for representative examples.",

keywords = "Compression algorithm, integral equations, moment methods",

author = "Yaniv Brick and Yilmaz, \{Ali E.\}",

note = "Publisher Copyright: {\textcopyright} 2016 IEEE.",

year = "2016",

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doi = "10.1109/TAP.2016.2617376",

language = "English",

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T1 - Fast Multilevel Computation of Low-Rank Representation of ℋ-Matrix Blocks

AU - Brick, Yaniv

AU - Yilmaz, Ali E.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - A physics-based algorithm for accelerating the computation of method of moments matrix blocks' low-rank approximation is presented. The algorithm relies on efficient sampling of phase- and amplitude-compensated interactions using nonuniform grids. Rank-revealing analysis is applied, in a multilevel fashion, to matrices of reduced column and row dimensions that describe subdomains' interactions with these coarse grids, rather than to the original matrix blocks. As a result, significant savings are achieved, especially for the inherently more compressible dynamic quasi-planar and quasi-static cases. The algorithm's reduced storage and computation time requirements are estimated analytically and verified numerically for representative examples.

AB - A physics-based algorithm for accelerating the computation of method of moments matrix blocks' low-rank approximation is presented. The algorithm relies on efficient sampling of phase- and amplitude-compensated interactions using nonuniform grids. Rank-revealing analysis is applied, in a multilevel fashion, to matrices of reduced column and row dimensions that describe subdomains' interactions with these coarse grids, rather than to the original matrix blocks. As a result, significant savings are achieved, especially for the inherently more compressible dynamic quasi-planar and quasi-static cases. The algorithm's reduced storage and computation time requirements are estimated analytically and verified numerically for representative examples.

KW - Compression algorithm

KW - integral equations

KW - moment methods

UR - https://www.scopus.com/pages/publications/85006262184

U2 - 10.1109/TAP.2016.2617376

DO - 10.1109/TAP.2016.2617376

M3 - Article

AN - SCOPUS:85006262184

SN - 0018-926X

VL - 64

SP - 5326

EP - 5334

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

IS - 12

M1 - 7590029

ER -

Fast Multilevel Computation of Low-Rank Representation of ℋ-Matrix Blocks

Abstract

Keywords

ASJC Scopus subject areas

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