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Mathematical and computational techniques for multilevel adaptive methods

Author: Ulrich Rüde; Society for Industrial and Applied Mathematics.
Publisher: Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1993.
Series: Frontiers in applied mathematics, 13.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Multilevel adaptive methods play an increasingly important role in the solution of many scientific and engineering problems. Fast adaptive methods techniques are widely used by specialists to execute and analyze simulation and optimization problems. This monograph presents a unified approach to adaptive methods, addressing their mathematical theory, efficient algorithms, and flexible data structures. Rüde  Read more...
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Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
(DLC) 93028379
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ulrich Rüde; Society for Industrial and Applied Mathematics.
ISBN: 9781611970968 1611970962
OCLC Number: 722473463
Notes: Title from title screen, viewed 04/05/2011.
Description: 1 electronic text (xii, 140 pages) : illustrations, digital file.
Contents: Chapter 1. Introduction. 1.1. Purpose and motivation; 1.2. Notation; 1.3. Basics and model problems --
Chapter 2. Multilevel splittings. 2.1. Abstract stable splittings; 2.2. Finite element spaces; 2.3. Stable bases; 2.4. Induced splittings; 2.5. Multilevel iterations; 2.6. Multilevel error estimators --
Chapter 3. The fully adaptive multigrid method. 3.1. Adaptive relaxation; 3.2. Algebraic structure; 3.3. Application of the theory of multilevel splittings; 3.4. Multilevel adaptive iteration; 3.5. Analysis of the V-cycle; 3.6. Hierarchical transformations; 3.7. Virtual global grids; 3.8. Robustness; 3.9. Parallelization; 3.10. Numerical examples; 3.11. Perspectives; 3.12. Historical remark --
Chapter 4. Data structures. 4.1. Introduction; 4.2. Finite element meshes; 4.3. Special cases; 4.4. Adaptive techniques; 4.5. Hierarchical meshes; 4.6. Implementation using C++ --
References --
Index.
Series Title: Frontiers in applied mathematics, 13.
Responsibility: Ulrich Rüde.

Abstract:

Multilevel adaptive methods play an increasingly important role in the solution of many scientific and engineering problems. Fast adaptive methods techniques are widely used by specialists to execute and analyze simulation and optimization problems. This monograph presents a unified approach to adaptive methods, addressing their mathematical theory, efficient algorithms, and flexible data structures. Rüde introduces a well-founded mathematical theory that leads to intelligent, adaptive algorithms, and suggests advanced software techniques. This new kind of multigrid theory supports the so-called "BPX" and "multilevel Schwarz" methods, and leads to the discovery of faster more robust algorithms. These techniques are deeply rooted in the theory of function spaces. Mathematical and Computational Techniques for Multilevel Adaptive Methods examines this development together with its implications for relevant algorithms for adaptive PDE methods. The author shows how abstract data types and object-oriented programming can be used for improved implementation.

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