Open Accessℋ 2 ‐matrix‐based fast volume integral equation solver for electrodynamic analysis
Author(s) -
Omar Saad,
Jiao Dan
Publication year - 2013
Publication title -
iet microwaves, antennas and propagation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.555
H-Index - 69
eISSN - 1751-8733
pISSN - 1751-8725
DOI - 10.1049/iet-map.2013.0090
Subject(s) - solver , interpolation (computer graphics) , matrix (chemical analysis) , integral equation , rank (graph theory) , reduction (mathematics) , operator (biology) , representation (politics) , mathematics , scaling , mathematical analysis , computer science , algorithm , mathematical optimization , physics , geometry , classical mechanics , materials science , motion (physics) , biochemistry , chemistry , combinatorics , repressor , politics , political science , transcription factor , law , composite material , gene
An ℋ 2 ‐matrix‐based mathematical framework is introduced and further developed to reduce the computational complexity of the volume integral equation (VIE)‐based analysis of electrodynamic problems. Numerical experiments have demonstrated a significant reduction in CPU time and memory consumption. A linear scaling with respect to matrix size in both CPU time and memory is achieved for small and medium‐sized electrodynamic problems with an interpolation‐based ℋ 2 ‐representation of the VIE operator in conjunction with a rank function for accuracy control. The proposed solver is applicable to arbitrarily shaped three‐dimensional structures immersed in inhomogeneous materials.