Wavelet Methods For Boundary Value Problems
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Wavelet Methods Elliptic Boundary Value Problems And Control Problems
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Author : Angela Kunoth
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Wavelet Methods Elliptic Boundary Value Problems And Control Problems written by Angela Kunoth 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.
Diese Monographie spannt einen Bogen rund um die aktuelle Thematik Wavelets, um neueste Entwicklungen anhand aufeinander aufbauender Probleme darzustellen und das konzeptuelle Potenzial von Waveletmethoden für Partielle Differentialgleichungen zu demonstrieren.
Wavelet Methods For Boundary Value Problems
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Author : Raymond R. Igharas
language : en
Publisher:
Release Date : 1997
Wavelet Methods For Boundary Value Problems written by Raymond R. Igharas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
Wavelet Methods Elliptic Boundary Value Problems And Control Problems
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Author : Angela Kunoth
language : en
Publisher:
Release Date : 2014-01-15
Wavelet Methods Elliptic Boundary Value Problems And Control Problems written by Angela Kunoth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Wavelet Methods For Elliptic Partial Differential Equations
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Author : Karsten Urban
language : en
Publisher: OUP Oxford
Release Date : 2008-11-27
Wavelet Methods For Elliptic Partial Differential Equations written by Karsten Urban and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-27 with Mathematics categories.
The origins of wavelets go back to the beginning of the last century and wavelet methods are by now a well-known tool in image processing (jpeg2000). These functions have, however, been used successfully in other areas, such as elliptic partial differential equations, which can be used to model many processes in science and engineering. This book, based on the author's course and accessible to those with basic knowledge of analysis and numerical mathematics, gives an introduction to wavelet methods in general and then describes their application for the numerical solution of elliptic partial differential equations. Recently developed adaptive methods are also covered and each scheme is complemented with numerical results, exercises, and corresponding software tools.
Multiscale Wavelet Methods For Partial Differential Equations
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Author : Wolfgang Dahmen
language : en
Publisher: Elsevier
Release Date : 1997-08-13
Multiscale Wavelet Methods For Partial Differential Equations written by Wolfgang Dahmen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-13 with Mathematics categories.
This latest volume in the Wavelets Analysis and Its Applications Series provides significant and up-to-date insights into recent developments in the field of wavelet constructions in connection with partial differential equations. Specialists in numerical applications and engineers in a variety of fields will find Multiscale Wavelet for Partial Differential Equations to be a valuable resource. Covers important areas of computational mechanics such as elasticity and computational fluid dynamics Includes a clear study of turbulence modeling Contains recent research on multiresolution analyses with operator-adapted wavelet discretizations Presents well-documented numerical experiments connected with the development of algorithms, useful in specific applications
Wavelet Least Square Methods For Boundary Value Problems
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Author : Wolfgang Dahmen
language : en
Publisher:
Release Date : 1999
Wavelet Least Square Methods For Boundary Value Problems written by Wolfgang Dahmen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
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.
Wavelet Based Numerical Methods For Some Boundary Value Problems
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Author : Xiaodi Wang
language : en
Publisher:
Release Date : 1995
Wavelet Based Numerical Methods For Some Boundary Value Problems written by Xiaodi Wang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Boundary value problems categories.
Implementation Of The Wavelet Galerkin Method For Boundary Value Problems
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Author : Adam K. Scheider
language : en
Publisher:
Release Date : 1998
Implementation Of The Wavelet Galerkin Method For Boundary Value Problems written by Adam K. Scheider and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Boundary value problems categories.
"The objective of this work is to develop a systematic method of implementing the Wavelet-Galerkin method for approximating solutions of differential equations. The beginning of this project included understanding what a wavelet is, and then becoming familiar with some of the applications. The Wavelet-Galerkin method, as applied in this paper, does not use a wavelet at all. In actuality, it uses the wavelet's scaling function. The distinction between the two will be given in the following sections of this paper. The sections of this thesis will include defining wavelets and their scaling functions. This will give the reader valued insight to wavelets and Discrete Wavelet Transforms (DWT). Following this will be a section defining the Galerkin method. The purpose of this section will be to give the reader an understanding of how weighted residual methods work, in particular, the Galerkin Method. Next will be a section on how Scaling functions will be implemented in the Galerkin method, forming the Wavelet-Galerkin Method. The focus of this investigation will deal with solutions to a basic homogeneous differential equation. The solution of this basic equation will be analyzed using three separate, distinct methods, and then the results will be compared. These methods include the Wavelet-Galerkin Method, the Galerkin Method using quadratic shape functions, and standard analytical means. Factors to be studied include computational time, effort, accuracy, and ease of implementing the method of solution. After a thorough comparison has been made, there will be a section to talk about possible applications of the Wavelet-Galerkin method and recommendations for future work. Predictions of what avenues to pursue in refining the Wavelet-Galerkin method will also be stated. And suggestions on how to make the method more accurate will be given."--Abstract.
Adaptive Wavelet Methods For Variational Formulations Of Nonlinear Elliptic Pdes On Tensor Product Domains
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Author : Roland Pabel
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2015-09-30
Adaptive Wavelet Methods For Variational Formulations Of Nonlinear Elliptic Pdes On Tensor Product Domains written by Roland Pabel and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-30 with Mathematics categories.
This thesis is concerned with the numerical solution of boundary value problems (BVPs) governed by nonlinear elliptic partial differential equations (PDEs). To iteratively solve such BVPs, it is of primal importance to develop efficient schemes that guarantee convergence of the numerically approximated PDE solutions towards the exact solution. The new adaptive wavelet theory guarantees convergence of adaptive schemes with fixed approximation rates. Furthermore, optimal, i.e., linear, complexity estimates of such adaptive solution methods have been established. These achievements are possible since wavelets allow for a completely new perspective to attack BVPs: namely, to represent PDEs in their original infinite dimensional realm. Wavelets in this context represent function bases with special analytical properties, e.g., the wavelets considered herein are piecewise polynomials, have compact support and norm equivalences between certain function spaces and the $ell_2$ sequence spaces of expansion coefficients exist. This theoretical framework is implemented in the course of this thesis in a truly dimensionally unrestricted adaptive wavelet program code, which allows one to harness the proven theoretical results for the first time when numerically solving the above mentioned BVPs. Numerical studies of 2D and 3D PDEs and BVPs demonstrate the feasibility and performance of the developed schemes. The BVPs are solved using an adaptive Uzawa algorithm, which requires repeated solution of nonlinear PDE sub-problems. This thesis presents for the first time a numerically competitive implementation of a new theoretical paradigm to solve nonlinear elliptic PDEs in arbitrary space dimensions with a complete convergence and complexity theory.