
Mathematical and Computational Techniques for Multilevel Adaptive Methods
Ulrich Ruede(Author)
Society for Industrial & Applied Mathematics,U.S. (Publisher)
Will be published approx. on 28. February 1994
Book
Paperback/Softback
152 pages
978-0-89871-320-6 (ISBN)
Description
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.
Ruede 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. This book 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.
Special Features:
Theory of multilevel (including additive) methods based on concepts in approximation theory and the theory of function spaces.
Fully adaptive multigrid, based on the ""virtual global grid"" refinement technique and the ""multilevel adaptive relaxation"" algorithm.
Ruede 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. This book 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.
Special Features:
Theory of multilevel (including additive) methods based on concepts in approximation theory and the theory of function spaces.
Fully adaptive multigrid, based on the ""virtual global grid"" refinement technique and the ""multilevel adaptive relaxation"" algorithm.
More details
Series
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Product notice
Paperback (trade)
Dimensions
Height: 254 mm
Width: 176 mm
Thickness: 11 mm
Weight
283 gr
ISBN-13
978-0-89871-320-6 (9780898713206)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
Chapter 1: Introduction. Purpose and motivation
Notation
Basics and model problems
Chapter 2: Multilevel Splittings. Abstract stable splittings
Finite element spaces
Stable bases
Induced splittings
Multilevel iterations
Multilevel error estimators
Chapter 3: The Fully Adaptive Multigrid Method. Adaptive relaxation
Algebraic structure
Application of the theory of multilevel splittings
Multilevel adaptive iteration
Analysis of the V cycle
Hierarchical transformations
Virtual global grids
Robustness
Parallelization
Numerical examples
Perspectives
Historical remark
Chapter 4: Data Structures. Introduction
Finite element meshes
Special cases
Adaptive techniques
Hierarchical meshes
Implementation using C++
References
Index.
Notation
Basics and model problems
Chapter 2: Multilevel Splittings. Abstract stable splittings
Finite element spaces
Stable bases
Induced splittings
Multilevel iterations
Multilevel error estimators
Chapter 3: The Fully Adaptive Multigrid Method. Adaptive relaxation
Algebraic structure
Application of the theory of multilevel splittings
Multilevel adaptive iteration
Analysis of the V cycle
Hierarchical transformations
Virtual global grids
Robustness
Parallelization
Numerical examples
Perspectives
Historical remark
Chapter 4: Data Structures. Introduction
Finite element meshes
Special cases
Adaptive techniques
Hierarchical meshes
Implementation using C++
References
Index.