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Analysis of algebraic multigrid parameters for two-dimensional steady-state heat diffusion equations

机译：二维稳态热扩散方程的代数多重网格参数分析

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摘要

In this work, it is provided a comparison for the algebraic multigrid (AMG) and the geometric multigrid (CMG) parameters, for Laplace and Poisson two-dimensional equations in square and triangular grids. The analyzed parameters are the number of: inner iterations in the solver, grids and unknowns. For the AMG, the effects of the grid reduction factor and the strong dependence factor in the coarse grid on the necessary CPU time are studied. For square grids the finite difference method is used, and for the triangular grids, the finite volume one. The results are obtained with the use of an adapted AMG1R6 code of Ruge and Stiiben. For the AMG the following components are used: standard coarsening, standard interpolation, correction scheme (CS), lexicographic Gauss-Seidel and V-cycle. Comparative studies among the CPU time of the GMG, AMG and singlegrid are made. It was verified that: (1) the optimum inner iterations is independent of the multigrid, however it is dependent on the grid; (2) the optimum number of grids is the maximum number; (3) AMG was shown to be sensitive to both the variation of the grid reduction factor and the strong dependence factor in the coarse grid; (4) in square grids, the GMG CPU time is 20% of the AMG one.
机译：在这项工作中，它提供了代数多重网格（AMG）和几何多重网格（CMG）参数的比较，以及正方形和三角形网格中的Laplace和Poisson二维方程的比较。分析的参数包括：求解器中的内部迭代，网格和未知数。对于AMG，研究了网格缩减因子和粗网格中的强依赖性因子对所需CPU时间的影响。对于正方形网格，使用有限差分法，对于三角形网格，使用有限体积一。使用改编的Ruge和Stiiben的AMG1R6代码可获得结果。对于AMG，使用以下组件：标准粗化，标准插值，校正方案（CS），字典高斯-赛德尔（Gauss-Seidel）和V循环。对GMG，AMG和singlegrid的CPU时间进行了比较研究。证明：（1）最佳内部迭代独立于多重网格，但取决于网格； （2）最佳网格数是最大网格数； （3）AMG对粗网格中的网格减小因子和强依赖性因子的变化均敏感。 （4）在方格中，GMG CPU时间是AMG的20％。

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  • 来源
    《Applied Mathematical Modelling》 |2012年第7期|p.2996-3006|共11页
  • 作者

    R. Suero; M.A.V. Pinto; C.H. Marchi; L.K.Araki; A.C. Alves;

  • 作者单位

    Federal Institute of Parana - Campus of Paranagua, 453 Antonio Carlos Rodrigues Street, 83215-750 Paranagua-PR, Brazil Federal University of Parana, Post-Craduate Course of Numerical Methods in Engineering, Centro Politecnico, 81531-980 Curitiba-PR, Brazil;

    Federal University of Parand, Department of Mechanical Engineering, Centro Politecnico, Block IV, 81531-980 Curitiba-PR, Brazil;

    Federal University of Parand, Department of Mechanical Engineering, Centro Politecnico, Block IV, 81531-980 Curitiba-PR, Brazil;

    Federal University of Parand, Department of Mechanical Engineering, Centro Politecnico, Block IV, 81531-980 Curitiba-PR, Brazil;

    Positivo University, Sector of Exact Sciences and Technology, 81280-330 Curitiba-PR, Brazil;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    parameters optimization; algebraic multigrid; square grids; triangular grids;

    机译：参数优化;代数多重网格方格三角形网格;

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