Study of additive correction multigrid application

Diego Fernando Moro¹; Carlos Henrique Marchi²

¹ Positivo University; ² Federal University of Paraná

doi:10.20906/CPS/CILAMCE2017-0953

Resumo

There are a lot of problems in engineering, some of them can be modeled through mathematical model equations without greater error addition. An analytical solution for these models equations are generally unknown, so one uses a numerical method to solve them. In this work, the Finite Volume Method (FVM) is employed to solve the following model equations: Burgers 1D, Poisson 2D and Poisson 3D. The linear system of equations resulted from FVM is solved using the Additive Correction Multigrid (ACM) strategy with Gauss-Seidel solver, the singlegrid is also tested and a comparison between them is shown. The coefficient of complexity, i.e., the rate which the CPU time increases in relation to the size of the grid doesn't reach exactly the unity, which is the theoretical complexity coefficient of Multigrid strategy, but a possible explanation to this fact is shown.

Palavras-chave: Additive Correction Multigrid; Finite Volume Method; Multigrid