A geometric multigrid method based on L-shaped coarsening for PDEs on stretched grids

作者：Bin Zubair H^*; MacLachlan S P; Oosterlee C W

来源：Numerical Linear Algebra with Applications, 2010, 17(6): 871-894.

DOI：10.1002/nla.665

• matrix-free multigrid
• grid-stretching
• L-shaped coarsening techniques
• cell-centred finite-volume method (FVM)

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.

• 出版日期2010-12