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

In this work, it is provided a comparison for the algebraic multigrid (AMG) and the geometric multigrid (GMG) 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 Stüben. 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.