ANALYSIS OF PARAMETERS OF GEOMETRIC MULTIGRID FOR THE CPU TIME FOR THREE-DIMENSIONAL POISSON EQUATION
Fabiane de Oliveira1; Sebastião Romero Franco2; Marcio Augusto Villela Pinto3
1 Universidade Estadual de Ponta Grossa.; 2 Universidade Estadual do Centro-Oeste.; 3 marcio_villela@ufpr.br
doi:10.20906/CPS/CILAMCE2017-0098
Resumo
The aim of this paper is to minimize the CPU time necessary for solving the 3D Poisson equation with Dirichlet boundary conditions. The Finite Difference Method is used to discretizate the differential equation with central differencing scheme. The systems of equations are solved with the lexicographic and red-black Gauss-Seidel methods associated to the geometric multigrid with correction scheme and V-cycle. It used trilinear interpolation and full coarsening with ratio r = 2. Comparisons are made among: (1) Restriction injection and full weighting; (2) Inner iteration number (v); (3) Number of mesh levels (L) and (4) unknowns number (N). With the analysis of algorithm complexity was possible to verify the optimum values this multigrid method in relation of optimization of CPU time.
Palavras-chave: Multigrid; finite difference method; 3D Poisson