Multilevel Projection Methods for Partial Differential Equations

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.