Wavelet Methods Elliptic Boundary Value Problems And Control 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 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.
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.
Splines And Pdes From Approximation Theory To Numerical Linear Algebra
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Author : Angela Kunoth
language : en
Publisher: Springer
Release Date : 2018-09-20
Splines And Pdes From Approximation Theory To Numerical Linear Algebra written by Angela Kunoth and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-20 with Mathematics categories.
This book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric methods. A wide variety of research topics are covered, ranging from approximation theory to structured numerical linear algebra. More precisely, the book provides (i) a self-contained introduction to B-splines, with special focus on approximation and hierarchical refinement, (ii) a broad survey of numerical schemes for control problems based on B-splines and B-spline-type wavelets, (iii) an exhaustive description of methods for computing and analyzing the spectral distribution of discretization matrices, and (iv) a detailed overview of the mathematical and implementational aspects of isogeometric analysis. The text is the outcome of a C.I.M.E. summer school held in Cetraro (Italy), July 2017, featuring four prominent lecturers with different theoretical and application perspectives. The book may serve both as a reference and an entry point into further research.
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 Nonlinear And Adaptive Approximation
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Author : Ronald DeVore
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-16
Multiscale Nonlinear And Adaptive Approximation written by Ronald DeVore 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 2009-09-16 with Mathematics categories.
The book of invited articles offers a collection of high-quality papers in selected and highly topical areas of Applied and Numerical Mathematics and Approximation Theory which have some connection to Wolfgang Dahmen's scientific work. On the occasion of his 60th birthday, leading experts have contributed survey and research papers in the areas of Nonlinear Approximation Theory, Numerical Analysis of Partial Differential and Integral Equations, Computer-Aided Geometric Design, and Learning Theory. The main focus and common theme of all the articles in this volume is the mathematics building the foundation for most efficient numerical algorithms for simulating complex phenomena.
A Multiplicative Schwartz Adaptive Wavelet Method For Elliptic Boundary Value Problems
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Author : Rob Stevenson
language : en
Publisher:
Release Date : 2008
A Multiplicative Schwartz Adaptive Wavelet Method For Elliptic Boundary Value Problems written by Rob Stevenson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Frontiers Of Numerical Analysis
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Author : James Blowey
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Frontiers Of Numerical Analysis written by James Blowey 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 2006-03-30 with Computers categories.
Contains lecture notes on four topics at the forefront of research in computational mathematics. This book presents a self-contained guide to a research area, an extensive bibliography, and proofs of the key results. It is suitable for professional mathematicians who require an accurate account of research in areas parallel to their own.
Fourier Bem
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Author : Fabian M.E. Duddeck
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-08-07
Fourier Bem written by Fabian M.E. Duddeck 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 2002-08-07 with Computers categories.
Like FEM, the Boundary Element Method (BEM) provides a general numerical tool for the solution of complex engineering problems. In the last decades, the range of its applications has remarkably been enlarged. Therefore dynamic and nonlinear problems can be tackled. However they still demand an explicit expression of a fundamental solution, which is only known in simple cases. In this respect, the present book proposes an alternative BEM-formulation based on the Fourier transform, which can be applied to almost all cases relevant in engineering mechanics. The basic principle is presented for the heat equation. Applications are taken from solid mechanics (e.g. poroelasticity, thermoelasticity). Transient and stationary examples are given as well as linear and nonlinear. Completed with a mathematical and mechanical glossary, the book will serve as a comprehensive text book linking applied mathematics to real world engineering problems.
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.