The induced dimension reduction (IDR) method of Sonneveld and van Gijzen [SIAM J. Sci. Comput 31(2008), pp. 1035-1062] is shown to be a Petrov-Galerkin (projection) method with a particular choice of left Krylov subspaces; these left subspaces are rational Krylov spaces. Consequently, other methods, such as BiCGStab and ML(s)BiCGStab, which are mathematically equivalent to some versions of IDR, can also be interpreted as Petrov-Galerkin methods. The connection with rational Krylov spaces inspired a new version of IDR, called Ritz-IDR, where the poles of the rational function are chosen as certain Ritz values. Experiments are presented illustrating the effectiveness of this new version.
Interpreting IDR as a Petrov-Galerkin method
SIMONCINI, VALERIA;
2010
Abstract
The induced dimension reduction (IDR) method of Sonneveld and van Gijzen [SIAM J. Sci. Comput 31(2008), pp. 1035-1062] is shown to be a Petrov-Galerkin (projection) method with a particular choice of left Krylov subspaces; these left subspaces are rational Krylov spaces. Consequently, other methods, such as BiCGStab and ML(s)BiCGStab, which are mathematically equivalent to some versions of IDR, can also be interpreted as Petrov-Galerkin methods. The connection with rational Krylov spaces inspired a new version of IDR, called Ritz-IDR, where the poles of the rational function are chosen as certain Ritz values. Experiments are presented illustrating the effectiveness of this new version.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
