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Multilevel Projection Methods for Partial Differential Equations

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by Stephen F. McCormick


1992 / vi + 114 pages / Softcover / ISBN: 978-0-898712-92-6 / List Price $49.00 / SIAM/CBMS Member Price $34.30 / Order Code CB62

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.

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.

ISBN: 9780898712926 

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