On the robustness of the multigrid method combining ILU and Partial Weight applied in an orthotropic diffusion problem

Abstract

This paper proposes an efficient and robust algorithm for solving a physical orthotropy problem. The algorithm is based on choosing the most efficient restriction operator and on an incomplete LU decomposition suited for each orthotropy direction. Local Fourier Analysis (LFA) is carried out in order to increase the efficiency of the multigrid method. Pure diffusion with orthotropy aligned to the coordinate axis x is the model considered. Equations are discretized by Finite Difference Method with uniform grid and second-order numerical scheme. Problems are solved with geometric multigrid method, correction scheme, V-cycle and standard coarsening ratio. The asymptotic convergence factor is calculated for different multigrid components, such as restriction operators, prolongation operators and solvers. Based on the optimum components obtained by LFA, we carried out experiments to analyze the complexity and computational cost of the algorithm proposed. The main conclusion is that the methodology proposed is efficient for the resolution of problems with strong orthotropy.