mg-tutorial

AMultigrid TutorialByWilliam L. BriggsPresented byVan Emden HensonCenter for Applied Scientific ComputingLawrence Livermore National LaboratoryThis work was performed, in part, under the auspices of the United States Department of Energy by Universityof California Lawrence Livermore National Laboratory under contract number W-7405-Eng-48.Outline•M odel Problems•P erformance, (cont)• Basic Iterative Schemes–Convergence– Convergence; experiments– Higher dimensions– Convergence; analysis– Experiments• Development of Multigrid• Some Theory– Coarse-grid correction– The spectral picture– Nested Iteration– The subspace picture– Restriction and Interpolation–The whole picture!– Standard cycles: MV, FMG• Complications•Performance– Anisotropic operators and grids– Implementation– Discontinuous or anisotropiccoefficients– storage and computation costs– Nonlinear Problems: FAS2 of 119Suggested Reading•Brandt, “Multi-level Adaptive Solutions to Boundary ValueProblems,” Math Comp., 31, 1977, pp 333-390.•Brandt, “1984 Guide to Multigrid Development, withapplications to computational fluid dynamics.”•Brigs, “A Multigrid Tutorial,” SIAM publications, 1987.nd• Briggs, Henson, and McCormick, “A Multigrid Tutorial, 2Edition,” SIAM publications, 2000.•Hackbusch, Multi-Grid Methods and Applications,” 1985.ackbusch and Trottenburg, “Multigrid Methods, Springer-Verlag, 1982”• Stüben and Trottenburg, “Multigrid Methods,” 1987.• Wesseling, “An ...