Wavelet-based Preconditioners for Boundary Integral Equations
Author: Thanh Tran
Publisher:
Published: 1996
Total Pages: 16
ISBN-13:
DOWNLOAD EBOOKPosts
Wavelet Based Fast Solution of Boundary Integral Equations
Author: Helmut Harbrecht
Publisher:
Published: 2006
Total Pages:
ISBN-13:
DOWNLOAD EBOOKWavelets Theory and Its Applications
Author: Mani Mehra
Publisher: Springer
Published: 2018-11-03
Total Pages: 185
ISBN-13: 9811325952
DOWNLOAD EBOOKThis 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.
Wavelet Methods — Elliptic Boundary Value Problems and Control Problems
Author: Angela Kunoth
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 150
ISBN-13: 332280027X
DOWNLOAD EBOOKDiese 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.
Schwarz Methods and Multilevel Preconditioners for Boundary Element Methods
Author: Ernst P. Stephan
Publisher:
Published: 2021
Total Pages: 0
ISBN-13: 9783030792848
DOWNLOAD EBOOKThis book provides a comprehensive examination of preconditioners for boundary element discretisations of first-kind integral equations. Focusing on domain-decomposition-type and multilevel methods, it allows readers to gain a good understanding of the mechanisms and necessary techniques in the analysis of the preconditioners. These techniques are unique for the discretisation of first-kind integral equations since the resulting systems of linear equations are not only large and ill-conditioned, but also dense. The book showcases state-of-the-art preconditioning techniques for boundary integral equations, presenting up-to-date research. It also includes a detailed discussion of Sobolev spaces of fractional orders to familiarise readers with important mathematical tools for the analysis. Furthermore, the concise overview of adaptive BEM, hp-version BEM, and coupling of FEM-BEM provides efficient computational tools for solving practical problems with applications in science and engineering.
Precondition for Boundary Integral Equations
Author: Cornell University. Department of Computer Science
Publisher:
Published: 1990
Total Pages: 21
ISBN-13:
DOWNLOAD EBOOKAbstract: "We propose new classes of preconditioners for the linear systems arising from a boundary integral equation method. The problem under consideration is Laplace's equation in three dimensions. The system arising in this context is dense and unsymmetric. Our preconditioners, which are based on solving small linear systems at each node, reduce the number of iterations in some cases by a factor of 20. Two iterative methods are considered: conjugate gradient on the normal equations and GMRES of Saad and Schultz. For a simple model problem, we demonstrate the exact relationship between the preconditioners and the resulting condition number of the system. Our analysis suggests that the condition number of the preconditioned system is decreased by a factor asymptotically greater than any constant."
Matrix Preconditioning Techniques and Applications
Author: Ke Chen
Publisher: Cambridge University Press
Published: 2005-07-14
Total Pages: 616
ISBN-13: 9780521838283
DOWNLOAD EBOOKA comprehensive introduction to preconditioning techniques, now an essential part of successful and efficient iterative solutions of matrices.
Wavelet Method for the Fast Resolution of 2-D Boundary Integral Equations
Author: Zhang Pingwen
Publisher:
Published: 1995
Total Pages: 16
ISBN-13:
DOWNLOAD EBOOKMultiscale Wavelet Methods for Partial Differential Equations
Author: Wolfgang Dahmen
Publisher:
Published: 1997
Total Pages: 570
ISBN-13: 0122006755
DOWNLOAD EBOOKThis 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. Key Features * 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
The Fast Solution of Boundary Integral Equations
Author: Sergej Rjasanow
Publisher: Springer Science & Business Media
Published: 2007-04-17
Total Pages: 285
ISBN-13: 0387340424
DOWNLOAD EBOOKThis book provides a detailed description of fast boundary element methods, all based on rigorous mathematical analysis. In particular, the authors use a symmetric formulation of boundary integral equations as well as discussing Galerkin discretisation. All the necessary related stability and error estimates are derived. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given.
