I. Perugia et V. Simoncini, Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations, NUM LIN ALG, 7(7-8), 2000, pp. 585-616
We are interested in the numerical solution of large structured indefinite
symmetric linear systems arising in mixed finite element approximations of
the magnetostatic problem; in particular, we analyse definite block-diagona
l and indefinite symmetric preconditioners. Relating the algebraic characte
ristics of the resulting preconditioned matrix to the properties of the con
tinuous problem and of its finite element discretization, we show that the
preconditioning strategies considered make the Krylov subspace solver used
insensitive to the mesh refinement parameter, in terms of the number of ite
rations. In order to achieve computational efficiency, we also analyse alge
braic approximations to the optimal preconditioners, and discuss their perf
ormance on real two- and three-dimensional application problems. Copyright
(C) 3000 John Wiley & Sons, Ltd.