COMPARISON OF THE PHYSICAL ANISOTROPY OF MULTIGRID METHOD FOR TWO-DIMENSIONAL DIFFUSION EQUATION
Grazielli Vassoler Rutz1; Marcio Augusto Villela Pinto2; Roberta Suero3
1 Federal Institute of Education, Science and Technology of Santa Catarina. Chapecó-SC, Brazil; 2 Federal University of Paraná, Departament of Mechanical Engineering. Curitiba - PR, Brazil.; 3 Federal Institute of Education, Science and Technology of Paraná. Campo Largo-PR, Brazil.
doi:10.20906/CPS/COB-2015-0506
Resumo
This work aims to analyze and optimize several multigrid parameters, while minimizing the CPU time in heat transfer problems that have anisotropy in the coefficients (physical anisotropy). The models considered are pure diffusion, that is, Poisson equation with anisotropy aligned with coordinate axis. For the discretization of the equation is used the finite difference method with uniform grids and numerical scheme of the second order (CDS) for the diffusive terms. The problems will be solved with the geometric multigrid method with Full Approximation Scheme (FAS) and V-Cycle with standard coarsening ratio (r=2), the restriction is given by injection and the prolongation by bilinear interpolation. In the solution of the equation system resulting from the discretization is used the MSI and GS as smoothing method. Several numerical experiments were carried out, varying the number of unknowns, inner iterations numbers and number of levels in the multigrid method. The main conclusion is that the anisotropy studied affects the performance of multigrid method, the CPU time and the order p of MSI and GS solvers.
Palavras-chave: Physical Anisotropy; Multigrid Parameters; Diffusion