Preconditioned Conjugate Gradient and Multigrid Methods for Numerical Solution of Multicomponent Mass Transfer Equations I. Diffusion-Reaction Equations

Abstract

In a series of two papers, we analyze the numerical performances of the preconditioned conjugate gradient algorithms (BICGSTAB and GMRES) and multigrid method in solving two-dimensional multicomponent mass transfer equations. The present test problems are steady-state, linear and nonlinear diffusion-reaction equations. The nonlinear algorithm used in connection with the preconditioned conjugate gradient methods is the modified Picard iteration. Theoretical results about the preconditioning are presented. The multigrid algorithm used is the Full Approximation Storage algorithm. The finite difference method was used to discretize the mathematical model equations. The numerical results obtained show good numerical performances.