Multilevel Projection Methods for Partial Differential Equations

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.