Multilevel projection methods for partial differential equations / Stephen F. McCormick.

Format:

Book

Author/Creator:

McCormick, S. F. (Stephen Fahrney), 1944-

Contributor:

Society for Industrial and Applied Mathematics.

Series:

CBMS-NSF regional conference series in applied mathematics ; 62.

CBMS-NSF regional conference series in applied mathematics ; 62

Language:

English

Subjects (All):

Differential equations, Partial--Numerical solutions.

Differential equations, Partial.

Multigrid methods (Numerical analysis).

Physical Description:

1 online resource (vi, 114 p. ) ill ;

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1992.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

The multilevel projection method is a new formalism that provides a framework for the development of multilevel algorithms in a very general setting. This methodology guides the choices of all the major multilevel processes, including relaxation and coarsening, and it applies directly to global or locally-refined discretizations. This book was developed from lectures at the CBMS-NSF Regional Conference on Multigrid and Multilevel Adaptive Methods for Partial Differential Equations in June 1991, and is a supplement to Multilevel Adaptive Methods for Partial Differential Equations, also written by Stephen F. McCormick.

Contents:

Chapter 1. Fundamentals. Introduction; Notation and conventions; Prototype problems; Discretization by projections; Realizability and nodal representations; Interlevel transfer matrices; Error measures

Chapter 2. Multilevel projections methods. Abstract framework: the Multilevel Projection method (PML); The Multigrid method (MG); the Fast Adaptive Composite grid method (FAC); Prototype problems; Relaxation; Coarse-level realizability and recursiveness; Parallelization: Asynchronous FAC (AFAC); Other practical matters; Summary

Chapter 3. Unigrid. Basic Unigrid scheme; Multgrid simulation; FAC simulation; Performance assessment; Caveats

Chapter 4. Paradigms. Rayleigh-Ritz 1: parameter estimation; Rayleigh-Ritz 2: transport equations: Galerkin 1: general Eigenvalue problems; Galerkin 2: Riccati equations; Petrov-Galerkin 1: the Finite Volume Element method (FVE); Petrov-Galerkin 2: image reconstruction

Chapter 5. Perspectives

References

Appendix A. Simple Unigrid code

Appendix B. More efficient Unigrid code

Appendix C. Modification to Unigrid code for local refinement.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Title from title screen, viewed 04/05/2011.

ISBN:

1-61197-009-1

Publisher Number:

CB62 SIAM