Optimal multilevel methods for H(grad), H(curl), and H(div) systems on graded and unstructured grids

Jinchao Xu, Long Chen, Ricardo H. Nochetto

Research output: Chapter in Book/Report/Conference proceedingChapter

41 Scopus citations

Abstract

We give an overview of multilevel methods, such as V-cycle multigrid and BPX preconditioner, for solving various partial differential equations (including H(grad), H(curl) and H(div) systems) on quasi-uniform meshes and extend them to graded meshes and completely unstructured grids. We first discuss the classical multigrid theory on the basis of the method of subspace correction of Xu and a key identity of Xu and Zikatanov. We next extend the classical multilevel methods in H(grad) to graded bisection grids upon employing the decomposition of bisection grids of Chen, Nochetto, and Xu. We finally discuss a class of multilevel preconditioners developed by Hiptmair and Xu for problems discretized on unstructured grids and extend them to H(curl) and H(div) systems over graded bisection grids.

Original languageEnglish (US)
Title of host publicationMultiscale, Nonlinear and Adaptive Approximation
Subtitle of host publicationDedicated to Wolfgang Dahmen on the Occasion of his 60th Birthday
PublisherSpringer Berlin Heidelberg
Pages599-659
Number of pages61
ISBN (Print)9783642034121
DOIs
StatePublished - Dec 1 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Optimal multilevel methods for H(grad), H(curl), and H(div) systems on graded and unstructured grids'. Together they form a unique fingerprint.

Cite this