Incomplete-leaf multilevel fast multipole algorithm for multiscale penetrable objects formulated with volume integral equations
Date
2017Source Title
IEEE Transactions on Antennas and Propagation
Print ISSN
0018-926X
Publisher
Institute of Electrical and Electronics Engineers Inc.
Volume
65
Issue
9
Pages
4914 - 4918
Language
English
Type
ArticleItem Usage Stats
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Abstract
Recently introduced incomplete-leaf (IL) tree structures for multilevel fast multipole algorithm (referred to as IL-MLFMA) is proposed for the analysis of multiscale inhomogeneous penetrable objects, in which there are multiple orders of magnitude differences among the mesh sizes. Considering a maximum Schaubert-Wilton-Glisson function population threshold per box, only overcrowded boxes are recursively divided into proper smaller boxes, leading to IL tree structures consisting of variable box sizes. Such an approach: 1) significantly reduces the CPU time for near-field calculations regarding overcrowded boxes, resulting a superior efficiency in comparison with the conventional MLFMA where fixed-size boxes are used and 2) effectively reduces the computational error of the conventional MLFMA for multiscale problems, where the protrusion of the basis/testing functions from their respective boxes dramatically impairs the validity of the addition theorem. Moreover, because IL-MLFMA is able to use deep levels safely and without compromising the accuracy, the memory consumption is significantly reduced compared with that of the conventional MLFMA. Several examples are provided to assess the accuracy and the efficiency of IL-MLFMA for multiscale penetrable objects.
Keywords
Incomplete leaf (IL)Multilevel fast multipole algorithm (MLFMA)
Multiscale problems
Volume integral equations (VIEs)