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A parallel multigrid solver for high‐frequency electromagnetic field analyses with small‐scale PC cluster
Author(s) -
Yosui Kuniaki,
Iwashita Takeshi,
Mori Michiya,
Kobayashi Eiichi
Publication year - 2008
Publication title -
electronics and communications in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.131
H-Index - 13
eISSN - 1942-9541
pISSN - 1942-9533
DOI - 10.1002/ecj.10160
Subject(s) - multigrid method , solver , computational science , block (permutation group theory) , computer science , finite element method , parallel computing , mathematics , scale (ratio) , convergence (economics) , algorithm , mathematical optimization , partial differential equation , geometry , physics , mathematical analysis , quantum mechanics , economics , thermodynamics , economic growth
Finite element analyses of electromagnetic fields are commonly used for designing various electronic devices. The scale of the analyses becomes larger and larger, therefore, a fast linear solver is needed to solve linear equations arising from the finite element method. Since a multigrid solver is the fastest linear solver for these problems, parallelization of a multigrid solver is quite a useful approach. From the viewpoint of industrial applications, an effective usage of a small‐scale PC cluster is important due to initial cost for introducing parallel computers. In this paper, a distributed parallel multigrid solver for a small‐scale PC cluster is developed. In high‐frequency electromagnetic analyses, a special block Gauss– Seidel smoother is used for the multigrid solver instead of general smoothers such as a Gauss– Seidel or Jacobi smoother in order to improve the convergence rate. The block multicolor ordering technique is applied to parallelize the smoother. A numerical example shows that a 3.7‐fold speed‐up in computational time and a 3.0‐fold increase in the scale of the analysis were attained when the number of CPUs was increased from one to five. © 2009 Wiley Periodicals, Inc. Electron Comm Jpn, 91(9): 28– 36, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/ecj.10160