PERFORMANCE OF A MULTIGRID ALGORITHM APPLIED TO POISSON EQUATION WITH ADDITIONAL DATA WITHIN THE DOMAIN OF THE TYPE
Neundorf, R. L. A.1; Pinto, M. A. V.2; Calvetti, L.1; Araki, L. K.2
1 Meteorological System of Paraná State SIMEPAR, Curitiba/PR, Brazil; 2 Federal University of Paraná, Department of Mechanical Engineering, Curitiba-PR, Brazil
doi:10.20906/CPS/COB-2015-0762
Resumo
This work aimed to study a methodology that integrates rainfall estimates gathered by satellite, radar and rain gauge measurements by solving numerically a Poisson equation. It has been found that by introducing rain gauge measurements as additional conditions on the domain, which is a requirement of this methodology, the multigrid method does not converge, a problem associated with small-scale singularities that are invisible on coarser grids, such as "small islands". In order to study this problem, we used the finite difference method (FDM) and a second-order accuracy Central Differencing Scheme (CDS) for the discretization of mathematical models. Gauss-Seidel method was used as solver. For all studied cases, numerical solutions were obtained by applying geometric multigrid method (GMG) with the following characteristics: correction scheme (CS), full-weighted restriction operator, prolongation by bilinear interpolation and the use of the maximum number of levels. The "small islands" problem was solved by imposing additional conditions on the domain, in an appropriate way, in all meshes used by the multigrid method. The results are considered positive because the multigrid method converges to the numerical solution of Poisson's Equation.
Palavras-chave: multigrid; iterative methods; finite difference method; small islands