Multilevel Projection Methods for Partial Differential Equations
Multilevel Projection Methods for Partial Differential Equations
Stephen F. McCormick, University of Colorado, Denver
June 1992
This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Paperback
9780898712926
£27.99
GBPPaperback
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.
Product details
June 1992Paperback
9780898712926
120 pages
252 × 172 × 11 mm
0.232kg
This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Table of Contents
- 1. Fundamentals. Introduction
- Notation and Conventions
- Prototype Problems
- Discretization by Projections
- Realizability and Nodal Representations
- Interlevel Transfer Matrices
- Error Measures
- 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
- 3. Unigrid. Basic Unigrid Scheme
- Multgrid Simulation
- FAC Simulation
- Performance Assessment
- Caveats
- 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
- 5. Perspectives. References
- Appendix A. Simple Unigrid Code
- Appendix B. More Efficient Unigrid Code
- Appendix C. Modification to Unigrid Code for Local Refinement.
