Preconditioning by Gram matrix approximation for diffusion-convection-reaction equations with discontinuous coefficients

Authors:
Gh. Juncu;C. Popa
Affiliations:
Politehnica University Bucharest, Catedra Inginerie Chimica, Polizu 1, 78126 Bucharest, Romania;Department of Mathematics, Ovidius University Constanta, Bl. Mamaia 124, 8700 Constanta, Romania
Venue:
Mathematics and Computers in Simulation
Year:
2002

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Abstract

This work analyses the preconditioning with Gram matrix approximation for the numerical solution of a linear convection-diffusion-reaction equation with discontinuous diffusion and reaction coefficients. The standard finite element method with piecewise linear test and trial functions on uniform meshes discretizes the equation. Three preconditioned conjugate gradient algorithms solve the discrete linear system: CGS, CGSTAB and GMRES. The preconditioning with Gram matrix approximation consists of replacing the solving of the equation with the preconditioner by two symmetric MG iterations. Numerical results are presented to assess the convergence behaviour of the preconditioning and to compare it with other preconditioners of multilevel type.