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      Error control of multiple-precision MLFMA

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      Author(s)
      Kalfa, M.
      Ergül, Ö.
      Ertürk, Vakur
      Date
      2018
      Source 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
      Article
      Item Usage Stats
      180
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      224
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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
      Diagonalization
      Error analysis
      Fast multipole method (FMM)
      Low-frequency breakdown
      Multiple-precision arithmetic (MPA)
      Permalink
      http://hdl.handle.net/11693/50244
      Published Version (Please cite this version)
      https://doi.org/10.1109/TAP.2018.2854405
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      • Department of Electrical and Electronics Engineering 4011
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