Wavelets in Numerical Simulation : Problem Adapted Construction and Applications - Karsten Urban

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Wavelets in Numerical Simulation

Problem Adapted Construction and Applications

By: Karsten Urban

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Paperback | 23 April 2002

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212 Pages

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Sapere aude! Immanuel Kant (1724-1804) Numerical simulations playa key role in many areas of modern science and technology. They are necessary in particular when experiments for the underlying problem are too dangerous, too expensive or not even possible. The latter situation appears for example when relevant length scales are below the observation level. Moreover, numerical simulations are needed to control complex processes and systems. In all these cases the relevant problems may become highly complex. Hence the following issues are of vital importance for a numerical simulation: - Efficiency of the numerical solvers: Efficient and fast numerical schemes are the basis for a simulation of 'real world' problems. This becomes even more important for realtime problems where the runtime of the numerical simulation has to be of the order of the time span required by the simulated process. Without efficient solution methods the simulation of many problems is not feasible. 'Efficient' means here that the overall cost of the numerical scheme remains proportional to the degrees of freedom, i. e. , the numerical approximation is determined in linear time when the problem size grows e. g. to upgrade accuracy. Of course, as soon as the solution of large systems of equations is involved this requirement is very demanding.

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Non-Fiction Medicine Medicine in General Mathematics Calculus & Mathematical Analysis Numerical Analysis Applied Mathematics Computing & I.T.Computer Science Functional Analysis & Transforms Engineering & Technology Technology in General

Engineering in General

Preface
Wavelet Bases	p. 1
Wavelet Bases in L[subscript 2] ([Omega])	p. 1
Wavelets on the Real Line	p. 12
Wavelets on the Interval	p. 17
Tensor Product Wavelets	p. 46
Wavelets on General Domains	p. 47
Vector Wavelets	p. 81
Wavelet Bases for H(div) and H(curl)	p. 83
Differentiation and Integration	p. 84
The Spaces H(div) and H(curl)	p. 90
Wavelet Systems for H(curl)	p. 92
Wavelet Bases for H(div)	p. 98
Helmholtz and Hodge Decompositions	p. 100
General Domains	p. 102
Applications	p. 109
Robust and Optimal Preconditioning	p. 109
Analysis and Simulation of Turbulent Flows	p. 118
Hardening of an Elastoplastic Rod	p. 138
References	p. 161
List of Figures	p. 169
List of Tables	p. 173
List of Symbols	p. 175
Index	p. 179
Table of Contents provided by Blackwell. All Rights Reserved.

Wavelets in Numerical Simulation

Problem Adapted Construction and Applications

At a Glance

Paperback

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How to return your order

Defective items

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