Analyses of low-order preconditioners on high-order schemes for some model problems
The author considers the two- and the three-dimensional Poisson equation on the unit square and cube, respectively, with Dirichlet boundary condition. In order to efficiently solve the system of linear algebraic equations obtained by high-order discretization, a preconditioned conjugate gradient method is suggested where a preconditioner is constructed on the base of low order schemes for the same differential equation. Tables of difference schemes of order 2, 4, 6 and a comparison between the condition numbers of preconditioned matrices for higher and lower schemes are presented. Proofs and practical examples are missing, however, and from the text of the paper does not follow that the proposed procedures are better than other known methods.
preconditioned conjugate gradient method
scientific article; zbMATH DE number 148457