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A geometric multigrid method based on L‐shaped coarsening for PDEs on stretched grids
Author(s) -
Bin Zubair H.,
MacLachlan S. P.,
Oosterlee C. W.
Publication year - 2010
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.665
Subject(s) - multigrid method , discretization , krylov subspace , mathematics , grid , context (archaeology) , relaxation (psychology) , mathematical optimization , partial differential equation , iterative method , algorithm , geometry , mathematical analysis , psychology , paleontology , social psychology , biology
In this work, we present a geometric multigrid method for PDEs discretized on stretched grids. The emphasis is on geometric L‐shaped coarsening techniques that we have developed in this context. The presented method is matrix free, in contrast with alternatives such as algebraic multigrid or certain preconditioned Krylov‐subspace‐based solution methods. For a Poisson model problem, we explain, both visually and in a descriptive way, how the stretched fine grid may yield a sequence of coarser grids so as to maintain the complementarity between relaxation and coarse grid correction. We also present complexity estimates of the method, thus demonstrating its efficiency. Through figures and numerical experiment tables, we provide convergence histories for the model problem discretized and solved on various stretched grids with our method. Copyright © 2009 John Wiley & Sons, Ltd.