Preconditioning by approximations of the Gram matrix for convection–diffusion equations

Gh. Juncu and C. Popa

Mathematics and Computers in Simulation (MATCOM), 1998, vol. 48, issue 2, 225-233

Abstract: The paper analyses the numerical performance of preconditioning with Gram matrix approximations for the solution of a convection–diffusion equation. The convection–diffusion equation is discretized on a rectangular grid by standard finite element methods with piecewise linear test and trial functions. The discrete linear system is solved by two different conjugate gradient algorithms: CGS and GMRES. The preconditioning with Gram matrix approximations consists of replacing the solving of the equation with the preconditioner by a few iterations of an appropriate iterative scheme. Two iterative algorithms are tested: incomplete Cholesky and multigrid. Numerical experiments indicate that these preconditioners are efficient at relatively small values of the Reynolds number.

Keywords: Preconditioning; Gram matrix; Incomplete Cholesky; Multigrid; Conjugate gradient; Convection–diffusion equation (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:48:y:1998:i:2:p:225-233

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