Multilevel Projection Methods for Partial Differential Equations
Will be published approx. on 30. June 1992
Book
Paperback/Softback
120 pages
978-0-89871-292-6 (ISBN)
Description
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.
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.
More details
Series
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Product notice
Paperback (trade)
Dimensions
Height: 252 mm
Width: 172 mm
Thickness: 11 mm
Weight
232 gr
ISBN-13
978-0-89871-292-6 (9780898712926)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
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.
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.