Error control of multiple-precision MLFMA
Date
2018Source Title
IEEE Transactions on Antennas and Propagation
Print ISSN
0018-926X
Electronic ISSN
1558-2221
Publisher
Institute of Electrical and Electronics Engineers
Volume
66
Issue
10
Pages
5651 - 5656
Language
English
Type
ArticleItem Usage Stats
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Abstract
We introduce and demonstrate a new error control scheme for the computation of far-zone interactions in the multilevel fast multipole algorithm when implemented within a multiple-precision arithmetic framework. The proposed scheme provides the optimum truncation numbers as well as the machine precisions given the desired relative error thresholds and the box sizes for the translation operator at all frequencies. In other words, unlike the previous error control schemes which are valid only for high-frequency problems, the proposed scheme can be used to control the error across both low- A nd high-frequency problems. Optimum truncation numbers and machine precisions are calculated for a wide range of box sizes and desired relative error thresholds with the proposed error control scheme. The results are compared with the previously available methods and numerical surveys.
Keywords
DiagonalizationError analysis
Fast multipole method (FMM)
Low-frequency breakdown
Multiple-precision arithmetic (MPA)