Wavelets Multilevel Methods And Elliptic Pdes
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Wavelets, Multilevel Methods, and Elliptic PDEs
Written at a level accessible to first-year graduate students, this book covers five major topics in numerical analysis: fast multipole methods, eigenvalue problems for differential equations, hierarchic modeling in mechanics, wavelets from filter banks, and multilevel methods. The authors are renowned experts and provide up-to-date overviews, complete with extensive bibliographies, along with new and previously unpublished material. Both students and experienced researchers will find this volume an ideal starting point for pursuing these important topics or applying the methods to their own research. The book contains proceedings from the seventh EPSRC Numerical Analysis Summer School, held in 1996.
Wavelet Methods for Elliptic Partial Differential Equations
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
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