Enhancing the Speed of the 3D Finite Element Analysis by the Geometric Multigrid Method With Edge Elements

概要

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This paper presents a fast electromagnetic field analysis by the 3D geometric multigrid method with edge elements. The multigrid method uses a symmetric Gauss-Seidel smoother with Conjugate Gradient acceleration. The convergence and computation speed of the V-cycle, W-cycle and full multigrid method using this smoother are compared with the conventional multigrid using Gauss-Seidel. Comparison is also made between the multigrid method and the ICCG method which is commonly used in the finite element analysis. The efficiency of the multigrid method is analyzed for meshes whose maximum aspect ratios vary in a wide range. It is proven that the multigrid method with the accelerated symmetric Gauss-Seidel outperforms the multigrid with Gauss-Seidel and the ICCG method. The multigrid method with the accelerated symmetric Gauss-Seidel shows stable convergence rate that does not deteriorate for bad quality meshes. It is robust against mesh distortion and parameter variations and is much faster than the conventional multigrid with Gauss-Seidel and the finite element method using ICCG.
社団法人電気学会の論文
2003-10-01