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

Gh. Juncu and C. Popa

Mathematics and Computers in Simulation (MATCOM), 2002, vol. 60, issue 6, 487-506

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.

Keywords: Gram matrix approximation; Diffusion–convection–reaction equation; Generalized conjugate gradient (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:60:y:2002:i:6:p:487-506

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