Numerical study of the performance of preconditioners based on algebraic multigrid method and approximate sparse inverses

Application of algebraic multigrid method and approximate sparse inverses are applied as preconditioners for large algebraic systems arising in approximation of diffusion-reaction problems in 3-dimensional complex domains. Here we report the results of numerical experiments when using highly graded and locally refined meshes for problems with non-homogeneous and anisotropic coefficients that have small features and almost singular solutions. For the discretization of the domain and the finite element approximation we have used the system AGGIEFEM, a universal computational tool for PDEs developed in the VIGRE seminar in Introduction to Scientific Computing at TAMU. For solving the algebraic system we have used ParaSails and BoomerAMG preconditioners that are part of the HYPRE (High Performance Preconditioners) library developed in CASC at Lawrence Livermore National Laboratory.