Overview

The main theme of the book centers around adaptive numerical schemes for conservation laws based on a concept of multiresolution analysis. Efficient algorithms are presented for implementing this program for finite volume schemes on unstructured grids for general systems of multidimensional hyperbolic conservation laws. The efficiency is verified for several realistic numerical test examples. In addition, a rather thorough error analysis is supporting the approach. The monograph covers material ranging from the mathematical theory of conservation laws to the nitty-gritty of hash tables and memory management for an actual implementation. This makes it a self-contained book for both numerical analysts interested in the construction and the theory of adapative finite volume schemes as well as for those looking for a detailed guide on how to design and implement adaptive wavelet based solvers for real world problems. Since modern techniques are presented in an appealing way, the material is also well suited for an advanced course in numerical mathematics.

Full Product Details

Author:   Siegfried Müller
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 2003
Volume:   27
Dimensions:   Width: 15.50cm , Height: 1.10cm , Length: 23.50cm
Weight:   0.670kg
ISBN:  

9783540443254

ISBN 10:   3540443258
Pages:   188
Publication Date:   11 December 2002
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Model Problem and Its Discretization.- 1.1 Conservation Laws.- 1.2 Finite Volume Methods.- 2 Multiscale Setting.- 2.1 Hierarchy of Meshes.- 2.2 Motivation.- 2.3 Box Wavelet.- 2.4 Change of Stable Completion.- 2.5 Box Wavelet with Higher Vanishing Moments.- 2.6 Multiscale Transformation.- 3 Locally Refined Spaces.- 3.1 Adaptive Grid and Significant Details.- 3.2 Grading.- 3.3 Local Multiscale Transformation.- 3.4 Grading Parameter.- 3.5 Locally Uniform Grids.- 3.6 Algorithms: Encoding, Thresholding, Grading, Decoding.- 3.7 Conservation Property.- 3.8 Application to Curvilinear Grids.- 4 Adaptive Finite Volume Scheme.- 4.1 Construction.- 4.2 A gorithms: Initial data, Prediction, Fluxes and Evolution.- 5 Error Analysis.- 5.1 Perturbation Error.- 5.2 Stability of Approximation.- 5.3 Reliability of Prediction.- 6 Data Structures and Memory Management.- 6.1 Algorithmic Requirements and Design Criteria.- 6.2 Hashing.- 6.3 Data Structures.- 7 Numerical Experiments.- 7.1 Parameter Studies.- 7.2 Real World Application.- A Plots of Numerical Experiments.- B The Context of Biorthogonal Wavelets.- B.1 General Setting.- B.1.1 Multiscale Basis.- B.1.2 Stable Completion.- B.1.3 Multiscale Transformation.- B.2 Biorthogonal Wavelets of the Box Function.- B.2.1 Haar Wavelets.- B.2.2 Biorthogonal Wavelets on the Real Line.- References.- List of Figures.- List of Tables.- Notation.

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