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Black-Box Preconditioning For Mixed Formulation . . . (2002)
BibTeX
@MISC{Powell02black-boxpreconditioning,
author = {Catherine E. Powell and David J. Silvester},
title = {Black-Box Preconditioning For Mixed Formulation . . . },
year = {2002}
}
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Abstract
Mixed finite element approximation of self-adjoint elliptic PDEs leads to symmetric indefinite linear systems of equations. Preconditioning strategies commonly focus on reduced symmetric positive definite systems and require nested iteration. This deficiency is avoided if preconditioned minres is applied to the full indefinite system. We outline such a preconditioning strategy, the key building block for which is a fast solver for a scalar diffusion operator based on black-box algebraic multigrid. Numerical results are presented for the Stokes equations arising in incompressible ow modelling and a variable diffusion equation that arises in modelling potential flow. We prove that the eigenvalues of the preconditioned matrices are contained in intervals that are bounded independently of the discretisation parameter and the PDE coefficients.
Keyphrases
mixed formulation black-box preconditioning self-adjoint elliptic pdes discretisation parameter potential flow reduced symmetric positive definite system variable diffusion equation require nested iteration numerical result black-box algebraic multigrid indefinite linear system preconditioned matrix preconditioning strategy incompressible ow modelling scalar diffusion operator mixed finite element approximation stokes equation key building block fast solver full indefinite system pde coefficient
