Mathematical and Computational Techniques for Multilevel Adaptive Methods - Brossura

Rüde, Ullrich

Brossura

ISBN 10: 089871320X ISBN 13: 9780898713206

Casa editrice: Society for Industrial and Applied Mathematics, 1987

Riassunto

This monograph presents a unified approach to adaptive methods, addressing their mathematical theory, efficient algorithms, and flexible data structures.

Su questo libro

Contenuti

1. Introduction. 1.1. Purpose and motivation; 1.2. Notation; 1.3. Basics and model problems; 2. Multilevel Splittings. 2.1. Abstract stable splittings; 2.2. Finite element spaces; 2.2.1. Approximation property, inverse property, and stable bases; 2.2.2. Besov norms; 2.2.3. Upper bounds; 2.2.4. Lower bounds; 2.2.5 Main theorem; 2.3. Stable bases; 2.4. Induced splittings; 2.5. Multilevel iterations; 2.6. Multilevel error estimators; 3. The Fully Adaptive Multigrid Method. 3.1. Adaptive relaxation; 3.1.1. Sequential adaptive relaxation; 3.1.2. Simultaneous adaptive relaxation; 3.1.3. Evaluation; 3.2. Algebraic structure; 3.3. Application of the theory of multilevel splittings; 3.4. Multilevel adaptive iteration; 3.4.1. Tracing dependencies between levels; 3.4.2. Cycling strategies; 3.4.3. Selection of the critical tolerances; 3.5. Analysis of the V-cycle; 3.6. Hierarchical transformations; 3.6.1. Hierarchical basis; 3.6.2. Efficient implementation of the multilevel adaptive iteration by hierarchical transformations; 3.7. Virtual global grids; 3.8. Robustness; 3.9. Parallelization; 3.10. Numerical examples; 3.10.1. Adaptive refinement at a re-entrant corner; 3.10.2. Virtual global grids and multilevel adaptive solution; 3.11. Perspectives; 3.12. Historical remark; 4. Data Structures. 4.1. Introduction; 4.1.1. Overview; 4.1.2. Relations; 4.1.3. Specification of software; 4.1.4. Efficiency and modularity; 4.2. Finite element meshes; 4.2.1. Classification; 4.2.2. Triangulations; 4.2.3. Topological structure of a finite element mesh; 4.2.4. Geometric structure; 4.2.5. Algebraic structure; 4.3. Special cases; 4.3.1. Uniform meshes; 4.3.2. Quasi-uniform meshes; 4.3.3. Piecewise uniform and quasi-discretionary unidiscretionary form meshes; 4.3.4. Unstructured meshes; 4.4. Adaptive techniques; 4.4.1. A-priori adaptivity; 4.4.2. Self-adaptive refinement; 4.4.3. Algorithmic eequirements; 4.4.4. Nested triangulations; 4.4.5. Regular refinement; 4.4.6. Refinement by bisection; 4.4.7. Self-adaptive refinement with uniform patches; 4.4.8. Virtual global grid refinement; 4.5. Hierarchical meshes; 4.5.1. Relations in the multilevel hierarchy; 4.5.2. Element-based data structures; 4.5.3. Node-based data structures; 4.5.4. Classification of nodes; 4.5.5. Semi-edges and connections; 4.5.6. Partially refined meshes; 4.5.7. Characteristic sets; 4.6. Implementation using C++; 4.6.1. Node classes; 4.6.2. Efficiency for special cases requiring limited mesh flexibility; 4.6.3. Virtual overloaded functions; 4.6.4. The role of C++; References; Index.

Dettagli dell'edizione

• Editore: Society for Industrial and Applied Mathematics
• Data di pubblicazione: 1987
• Lingua: Inglese
• ISBN 10: 089871320X
• ISBN 13: 9780898713206
• Rilegatura: Copertina flessibile
• Numero di pagine: 152
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile