Wavelet Methods — Elliptic Boundary Value Problems and Control Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Wavelet Methods — Elliptic Boundary Value Problems and Control Problems write by Angela Kunoth. This book was released on 2012-12-06. Wavelet Methods — Elliptic Boundary Value Problems and Control Problems available in PDF, EPUB and Kindle. 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
Wavelet Methods - Elliptic Boundary Value Problems and Control Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Wavelet Methods - Elliptic Boundary Value Problems and Control Problems write by Angela Kunoth. This book was released on 2014-01-15. Wavelet Methods - Elliptic Boundary Value Problems and Control Problems available in PDF, EPUB and Kindle.
Wavelet Methods for Elliptic Partial Differential Equations
Wavelet Methods for Elliptic Partial Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Wavelet Methods for Elliptic Partial Differential Equations write by Karsten Urban. This book was released on 2008-11-27. Wavelet Methods for Elliptic Partial Differential Equations available in PDF, EPUB and Kindle. 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.
Adaptive Wavelet Methods for Variational Formulations of Nonlinear Elliptic PDEs on Tensor-Product Domains
Adaptive Wavelet Methods for Variational Formulations of Nonlinear Elliptic PDEs on Tensor-Product Domains - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Adaptive Wavelet Methods for Variational Formulations of Nonlinear Elliptic PDEs on Tensor-Product Domains write by Roland Pabel. This book was released on 2015-09-30. Adaptive Wavelet Methods for Variational Formulations of Nonlinear Elliptic PDEs on Tensor-Product Domains available in PDF, EPUB and Kindle. 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
Splines and PDEs: From Approximation Theory to Numerical Linear Algebra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Splines and PDEs: From Approximation Theory to Numerical Linear Algebra write by Angela Kunoth. This book was released on 2018-09-20. Splines and PDEs: From Approximation Theory to Numerical Linear Algebra available in PDF, EPUB and Kindle. 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.
