Wavelets In Numerical Simulation
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Wavelets In Numerical Simulation
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Author : Karsten Urban
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Wavelets In Numerical Simulation written by Karsten Urban and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Numerical Analysis Of Wavelet Methods
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Author : A. Cohen
language : en
Publisher: Elsevier
Release Date : 2003-04-29
Numerical Analysis Of Wavelet Methods written by A. Cohen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-29 with Mathematics categories.
Since their introduction in the 1980's, wavelets have become a powerful tool in mathematical analysis, with applications such as image compression, statistical estimation and numerical simulation of partial differential equations. One of their main attractive features is the ability to accurately represent fairly general functions with a small number of adaptively chosen wavelet coefficients, as well as to characterize the smoothness of such functions from the numerical behaviour of these coefficients. The theoretical pillar that underlies such properties involves approximation theory and function spaces, and plays a pivotal role in the analysis of wavelet-based numerical methods. This book offers a self-contained treatment of wavelets, which includes this theoretical pillar and it applications to the numerical treatment of partial differential equations. Its key features are:1. Self-contained introduction to wavelet bases and related numerical algorithms, from the simplest examples to the most numerically useful general constructions.2. Full treatment of the theoretical foundations that are crucial for the analysisof wavelets and other related multiscale methods : function spaces, linear and nonlinear approximation, interpolation theory.3. Applications of these concepts to the numerical treatment of partial differential equations : multilevel preconditioning, sparse approximations of differential and integral operators, adaptive discretization strategies.
Wavelet Numerical Method And Its Applications In Nonlinear Problems
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Author : You-He Zhou
language : en
Publisher: Springer Nature
Release Date : 2021-03-09
Wavelet Numerical Method And Its Applications In Nonlinear Problems written by You-He Zhou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-09 with Technology & Engineering categories.
This book summarizes the basic theory of wavelets and some related algorithms in an easy-to-understand language from the perspective of an engineer rather than a mathematician. In this book, the wavelet solution schemes are systematically established and introduced for solving general linear and nonlinear initial boundary value problems in engineering, including the technique of boundary extension in approximating interval-bounded functions, the calculation method for various connection coefficients, the single-point Gaussian integration method in calculating the coefficients of wavelet expansions and unique treatments on nonlinear terms in differential equations. At the same time, this book is supplemented by a large number of numerical examples to specifically explain procedures and characteristics of the method, as well as detailed treatments for specific problems. Different from most of the current monographs focusing on the basic theory of wavelets, it focuses on the use of wavelet-based numerical methods developed by the author over the years. Even for the necessary basic theory of wavelet in engineering applications, this book is based on the author’s own understanding in plain language, instead of a relatively difficult professional mathematical description. This book is very suitable for students, researchers and technical personnel who only want to need the minimal knowledge of wavelet method to solve specific problems in engineering.
A First Course In Wavelets With Fourier Analysis
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Author : Albert Boggess
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-20
A First Course In Wavelets With Fourier Analysis written by Albert Boggess and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-20 with Mathematics categories.
A comprehensive, self-contained treatment of Fourier analysis and wavelets—now in a new edition Through expansive coverage and easy-to-follow explanations, A First Course in Wavelets with Fourier Analysis, Second Edition provides a self-contained mathematical treatment of Fourier analysis and wavelets, while uniquely presenting signal analysis applications and problems. Essential and fundamental ideas are presented in an effort to make the book accessible to a broad audience, and, in addition, their applications to signal processing are kept at an elementary level. The book begins with an introduction to vector spaces, inner product spaces, and other preliminary topics in analysis. Subsequent chapters feature: The development of a Fourier series, Fourier transform, and discrete Fourier analysis Improved sections devoted to continuous wavelets and two-dimensional wavelets The analysis of Haar, Shannon, and linear spline wavelets The general theory of multi-resolution analysis Updated MATLAB code and expanded applications to signal processing The construction, smoothness, and computation of Daubechies' wavelets Advanced topics such as wavelets in higher dimensions, decomposition and reconstruction, and wavelet transform Applications to signal processing are provided throughout the book, most involving the filtering and compression of signals from audio or video. Some of these applications are presented first in the context of Fourier analysis and are later explored in the chapters on wavelets. New exercises introduce additional applications, and complete proofs accompany the discussion of each presented theory. Extensive appendices outline more advanced proofs and partial solutions to exercises as well as updated MATLAB routines that supplement the presented examples. A First Course in Wavelets with Fourier Analysis, Second Edition is an excellent book for courses in mathematics and engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for mathematicians, signal processing engineers, and scientists who wish to learn about wavelet theory and Fourier analysis on an elementary level.
Wavelet Analysis And Applications
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Author : Tao Qian
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-02-24
Wavelet Analysis And Applications written by Tao Qian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-24 with Mathematics categories.
This volume reflects the latest developments in the area of wavelet analysis and its applications. Since the cornerstone lecture of Yves Meyer presented at the ICM 1990 in Kyoto, to some extent, wavelet analysis has often been said to be mainly an applied area. However, a significant percentage of contributions now are connected to theoretical mathematical areas, and the concept of wavelets continuously stretches across various disciplines of mathematics. Key topics: Approximation and Fourier Analysis Construction of Wavelets and Frame Theory Fractal and Multifractal Theory Wavelets in Numerical Analysis Time-Frequency Analysis Adaptive Representation of Nonlinear and Non-stationary Signals Applications, particularly in image processing Through the broad spectrum, ranging from pure and applied mathematics to real applications, the book will be most useful for researchers, engineers and developers alike.
Numerical Simulation Of Turbulent Flows And Noise Generation
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Author : Christophe Brun
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-07
Numerical Simulation Of Turbulent Flows And Noise Generation written by Christophe Brun and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-07 with Technology & Engineering categories.
Large Eddy Simulation (LES) is a high-fidelity approach to the numerical simulation of turbulent flows. Recent developments have shown LES to be able to predict aerodynamic noise generation and propagation as well as the turbulent flow, by means of either a hybrid or a direct approach. This book is based on the results of two French/German research groups working on LES simulations in complex geometries and noise generation in turbulent flows. The results provide insights into modern prediction approaches for turbulent flows and noise generation mechanisms as well as their use for novel noise reduction concepts.
Wavelets
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Author : John J. Benedetto
language : en
Publisher: CRC Press
Release Date : 2021-07-28
Wavelets written by John J. Benedetto and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-28 with Mathematics categories.
Wavelets is a carefully organized and edited collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. The construction of wavelet bases and the fast computation of the wavelet transform in both continuous and discrete settings is covered. The theory of frames, dilation equations, and local Fourier bases are also presented. The second part of the book discusses applications in signal analysis, while the third part covers operator analysis and partial differential equations. Each chapter in these sections provides an up-to-date introduction to such topics as sampling theory, probability and statistics, compression, numerical analysis, turbulence, operator theory, and harmonic analysis. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. It will be an especially useful reference for harmonic analysts, partial differential equation researchers, signal processing engineers, numerical analysts, fluids researchers, and applied mathematicians.
Wavelets In Electromagnetics And Device Modeling
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Author : George W. Pan
language : en
Publisher: John Wiley & Sons
Release Date : 2003-04-10
Wavelets In Electromagnetics And Device Modeling written by George W. Pan and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-10 with Science categories.
Thema des Buches ist die Elementarwellen- (Wavelet-) -Theorie (Zeit-Frequenz-Analyse), ein Grenzgebiet zwischen Mathematik und Ingenieurwissenschaften. - viele Anwendungen in der Elektronik, darunter Antennentheorie und drahtlose Kommunikation - erstes Buch, das die Wavelet-Theorie auf elektromagnetische Phänomene und auf die Modellierung von Halbleiterbauelementen anwendet
Ten Lectures On Wavelets
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Author : Ingrid Daubechies
language : en
Publisher: SIAM
Release Date : 1992-01-01
Ten Lectures On Wavelets written by Ingrid Daubechies and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Science categories.
Wavelets are a mathematical development that may revolutionize the world of information storage and retrieval according to many experts. They are a fairly simple mathematical tool now being applied to the compression of data--such as fingerprints, weather satellite photographs, and medical x-rays--that were previously thought to be impossible to condense without losing crucial details. This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. The author has worked on several aspects of the wavelet transform and has developed a collection of wavelets that are remarkably efficient.