Recursive Krylov-based multigrid cycles

摘要: We consider multigrid (MG) cycles based on the recursive use of a two-grid method, in which coarse-grid system is solved by μ>1 steps Krylov subspace iterative method. The approach further extended allowing such inner iterations only at levels given multiplicity, whereas V-cycle formulation used all other levels. For symmetric positive definite systems and MG schemes, we flexible (or generalized) conjugate gradient method as solver for both outer iterations. Then, some algebraic (block matrix) properties viewed preconditioner, show that can have optimal convergence if μ chosen to be sufficiently large. also formulate conditions guarantee both, complexity convergence, bounded independently number Our analysis shows is, least, effective standard W-cycle, numerical results illustrate it much faster than latter, actually more robust predicted theory. Copyright © 2007 John Wiley & Sons, Ltd.