A parallel multigrid solver for high‐frequency electromagnetic field analyses with small‐scale PC cluster

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