Mathematical and computational techniques for multilevel adaptive methods / Ulrich Rüde.

Format:

Book

Author/Creator:

Rüde, Ulrich.

Contributor:

Society for Industrial and Applied Mathematics.

Series:

Frontiers in applied mathematics ; 13.

Frontiers in applied mathematics ; vol. 13

Language:

English

Subjects (All):

Differential equations, Partial--Numerical solutions.

Differential equations, Partial.

Multigrid methods (Numerical analysis).

Physical Description:

1 electronic text (xii, 140 p.) : ill., digital file.

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1993.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

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 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.

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. 129-134) and index.

Title from title screen, viewed 04/05/2011.

ISBN:

1-61197-096-2

Publisher Number:

FR13 SIAM