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Author : S. Bertoluzza
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (639 download)
Download or read book A Dynamically Adaptive Wavelet Method for Solving Partial Differential Equations written by S. Bertoluzza and published by . This book was released on 1992 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Karsten Urban
Publisher : OUP Oxford
ISBN 13 : 0191523526
Total Pages : 512 pages
Book Rating : 4.1/5 (915 download)
Download or read book Wavelet Methods for Elliptic Partial Differential Equations written by Karsten Urban and published by OUP Oxford. This book was released on 2008-11-27 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Roland Pabel
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832541020
Total Pages : 336 pages
Book Rating : 4.8/5 (325 download)
Download or read book Adaptive Wavelet Methods for Variational Formulations of Nonlinear Elliptic PDEs on Tensor-Product Domains written by Roland Pabel and published by Logos Verlag Berlin GmbH. This book was released on 2015-09-30 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Karsten Urban
Publisher : Numerical Mathematics and Scie
ISBN 13 : 0198526059
Total Pages : 509 pages
Book Rating : 4.1/5 (985 download)
Download or read book Wavelet Methods for Elliptic Partial Differential Equations written by Karsten Urban and published by Numerical Mathematics and Scie. This book was released on 2009 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelet methods are by now a well-known tool in image processing (jpeg2000). These functions have been used successfully in other areas, however. Elliptic Partial Differential Equations which model several processes in, for example, science and engineering, is one such field. This book, based on the author's course, 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.
Author : Stephan Dahlke
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (749 download)
Download or read book An Adaptive Wavelet Method for Parameter Identication Problems in Parabolic Partial Differential Equations written by Stephan Dahlke and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wolfgang Dahmen
Publisher : Elsevier
ISBN 13 : 0080537146
Total Pages : 587 pages
Book Rating : 4.0/5 (85 download)
Download or read book Multiscale Wavelet Methods for Partial Differential Equations written by Wolfgang Dahmen and published by Elsevier. This book was released on 1997-08-13 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : Petru A. Cioica
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (744 download)
Download or read book Adaptive Wavelet Methods for Elliptic Stochastic Partial Differential Equations written by Petru A. Cioica and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dominik Lellek
Publisher :
ISBN 13 : 9783832540678
Total Pages : 0 pages
Book Rating : 4.5/5 (46 download)
Download or read book Adaptive Wavelet Schwarz Methods for Nonlinear Elliptic Partial Differential Equations written by Dominik Lellek and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adaptive wavelet methods have recently proven to be a very powerful instrument for the numerical treatment of nonlinear partial differential equations. In many cases, these methods can be shown to converge with an optimal rate with respect to the degrees of freedom and in linear complexity. In this thesis, we couple such algorithms with nonlinear Schwarz domain decomposition techniques. With this approach, we can develop efficient parallel adaptive wavelet Schwarz methods for a class of nonlinear problems and prove their convergence and optimality. We support the theoretical findings with instructive numerical experiments. In addition, we present how these techniques can be applied to the stationary, incompressible Navier-Stokes equation. Furthermore, we couple the adaptive wavelet Schwarz methods with a Newton-type method.
Download or read book התפתחיות תאורטיות ואמפיריות בויקטימולוגיה written by and published by . This book was released on 1973 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ülo Lepik
Publisher : Springer Science & Business Media
ISBN 13 : 3319042955
Total Pages : 209 pages
Book Rating : 4.3/5 (19 download)
Download or read book Haar Wavelets written by Ülo Lepik and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems. Haar wavelet-based solutions for a wide range of problems, such as various differential and integral equations, fractional equations, optimal control theory, buckling, bending and vibrations of elastic beams are considered. Numerical examples demonstrating the efficiency and accuracy of the Haar method are provided for all solutions.
Author : Claude Jeffrey Gittelson
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (95 download)
Download or read book Adaptive Wavelet Methods for Elliptic Partial Differential Equations with Random Operators written by Claude Jeffrey Gittelson and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. Cohen
Publisher : Elsevier
ISBN 13 : 0080537855
Total Pages : 357 pages
Book Rating : 4.0/5 (85 download)
Download or read book Numerical Analysis of Wavelet Methods written by A. Cohen and published by Elsevier. This book was released on 2003-04-29 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 analysis of 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.
Author : Silvia Bertoluzza
Publisher : Springer Science & Business Media
ISBN 13 : 364224078X
Total Pages : 324 pages
Book Rating : 4.6/5 (422 download)
Download or read book Multiscale and Adaptivity: Modeling, Numerics and Applications written by Silvia Bertoluzza and published by Springer Science & Business Media. This book was released on 2012-01-07 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of lecture notes for the CIME course on "Multiscale and Adaptivity: Modeling, Numerics and Applications," held in Cetraro (Italy), in July 2009. Complex systems arise in several physical, chemical, and biological processes, in which length and time scales may span several orders of magnitude. Traditionally, scientists have focused on methods that are particularly applicable in only one regime, and knowledge of the system on one scale has been transferred to another scale only indirectly. Even with modern computer power, the complexity of such systems precludes their being treated directly with traditional tools, and new mathematical and computational instruments have had to be developed to tackle such problems. The outstanding and internationally renowned lecturers, coming from different areas of Applied Mathematics, have themselves contributed in an essential way to the development of the theory and techniques that constituted the subjects of the courses.
Author : Houman Owhadi
Publisher : Cambridge University Press
ISBN 13 : 1108588042
Total Pages : 491 pages
Book Rating : 4.1/5 (85 download)
Download or read book Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization written by Houman Owhadi and published by Cambridge University Press. This book was released on 2019-10-24 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although numerical approximation and statistical inference are traditionally covered as entirely separate subjects, they are intimately connected through the common purpose of making estimations with partial information. This book explores these connections from a game and decision theoretic perspective, showing how they constitute a pathway to developing simple and general methods for solving fundamental problems in both areas. It illustrates these interplays by addressing problems related to numerical homogenization, operator adapted wavelets, fast solvers, and Gaussian processes. This perspective reveals much of their essential anatomy and greatly facilitates advances in these areas, thereby appearing to establish a general principle for guiding the process of scientific discovery. This book is designed for graduate students, researchers, and engineers in mathematics, applied mathematics, and computer science, and particularly researchers interested in drawing on and developing this interface between approximation, inference, and learning.
Author : Mani Mehra
Publisher : Springer
ISBN 13 : 9811325952
Total Pages : 185 pages
Book Rating : 4.8/5 (113 download)
Download or read book Wavelets Theory and Its Applications written by Mani Mehra and published by Springer. This book was released on 2018-11-03 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides comprehensive information on the conceptual basis of wavelet theory and it applications. Maintaining an essential balance between mathematical rigour and the practical applications of wavelet theory, the book is closely linked to the wavelet MATLAB toolbox, which is accompanied, wherever applicable, by relevant MATLAB codes. The book is divided into four parts, the first of which is devoted to the mathematical foundations. The second part offers a basic introduction to wavelets. The third part discusses wavelet-based numerical methods for differential equations, while the last part highlights applications of wavelets in other fields. The book is ideally suited as a text for undergraduate and graduate students of mathematics and engineering.
Author : David B. Anderson
Publisher :
ISBN 13 :
Total Pages : 202 pages
Book Rating : 4.:/5 (384 download)
Download or read book A Wavelet Based Spatially and Temporally Adaptive Nmerical Method for Partial Differential Equations and Its Application to the Solution of the Heatflow Problem in Crystal Growth written by David B. Anderson and published by . This book was released on 1996 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David B. Anderson
Publisher :
ISBN 13 :
Total Pages : 404 pages
Book Rating : 4.:/5 (85 download)
Download or read book A Wavelet Based Spatially and Temporally Adaptive Numerical Method for Partial Differential Equations and Its Application to the Solution of the Heatflow Problem in Crystal Growth written by David B. Anderson and published by . This book was released on 1996 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt:
