Stochastic Estimation of the Frobenius Norm in the ACA Convergence Criterion

Author

Heldring, A. ; Ubeda, E. ; Rius, J.M.

Author_Institution

Dept. of Signal Process. & Telecommun., Univ. Politec. de Catalunya, Barcelona, Spain

Volume

63

Issue

3

fYear

2015

fDate

Mar-15

Firstpage

1155

Lastpage

1158

Abstract

The adaptive cross approximation (ACA) algorithm has been used in many fast Integral Equation solvers for electromagnetic Radiation and Scattering problems. It efficiently computes a low rank approximation to the interaction matrix between mutually distant parts of a scattering object. The ACA is an iterative algorithm that needs an accurate and efficient convergence criterion. The evaluation of this criterion may consume a considerable part of the computational resources. This communication presents an efficient new way to evaluate the convergence criterion, using a stochastic approach.

Keywords

approximation theory; convergence of numerical methods; electromagnetic wave scattering; integral equations; iterative methods; matrix algebra; stochastic processes; ACA convergence criterion; Frobenius norm; adaptive cross approximation algorithm; computational resources; convergence criterion; electromagnetic radiation; electromagnetic scattering problems; fast integral equation solvers; interaction matrix; iterative algorithm; low rank approximation; scattering object; stochastic estimation approach; Approximation algorithms; Approximation methods; Convergence; Estimation; Kernel; Scattering; Standards; Adaptive cross approximation (ACA); computational electromagnetics; method of moments;

fLanguage

English

Journal_Title

Antennas and Propagation, IEEE Transactions on

Publisher

ieee

ISSN

0018-926X

Type

jour

DOI

10.1109/TAP.2014.2386306

Filename

6998920