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Wavelet Methods for Elliptic Partial Differential Equations

Karsten Urban

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.001.0001
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

Wavelets have become a powerful tool in several applications by now. Their use for the numerical solution of operator equations has been investigated more recently. By now the theoretical ... More


Wavelets

Karsten Urban

in Wavelet Methods for Elliptic Partial Differential Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.003.0005
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

Starting from a Multiresolution Analysis, wavelets are introduced as a basis for the corresponding detail spaces. The main families are introduced, namely orthogonal Daubechies' wavelets as well as ... More


Variational methods for wavelets, with S. Dahlke

Klaus Böhmer

in Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577040
eISBN:
9780191595172
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577040.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 9 studies S. Dahlke studies wavelet methods. This is the first presentation in this generality and is appropriate for nonlinear problems and bifurcation for elliptic PDEs. As a consequence of ... More


Wavelet-Galerkin Methods

Karsten Urban

in Wavelet Methods for Elliptic Partial Differential Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.003.0006
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

Using wavelets as basis for the test and trial spaces of a Galerkin method allows an optimal preconditioning of the stiffness matrix. It is proven that a diagonal scaling provides such a ... More


Wavelets on General Domains

Karsten Urban

in Wavelet Methods for Elliptic Partial Differential Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.003.0008
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

The construction of wavelets on general domains is performed in three steps. This chapter starts by introducing the construction of scaling functions and wavelets on bounded univariate intervals. ... More


Introduction

Karsten Urban

in Wavelet Methods for Elliptic Partial Differential Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.003.0001
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

This chapter gives an outline of the history of wavelets, in particular with respect to their use to numerically solve partial differential equations. The scope of the book and its outline is ... More


Adaptive Wavelet Methods

Karsten Urban

in Wavelet Methods for Elliptic Partial Differential Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.003.0007
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

This chapter starts by adaptively approximating a given function and introduce the main theoretical concepts. After describing the more classical approach to adaptivity based upon a-posteriori error ... More


Some Applications

Karsten Urban

in Wavelet Methods for Elliptic Partial Differential Equations

Published in print:
2008
Published Online:
May 2009
ISBN:
9780198526056
eISBN:
9780191712340
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526056.003.0009
Subject:
Mathematics, Applied Mathematics, Mathematical Finance

Some recent applications of wavelet methods are shown. The chapter starts with the numerical realization of the WEM and consider the L-shaped domain as a model for a non-separable domain. The chapter ... More


Numerical Methods for Nonlinear Elliptic Differential Equations: A Synopsis

Klaus Boehmer

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199577040
eISBN:
9780191595172
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577040.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, and create an exciting interplay. Other books discuss nonlinearity by a very few important ... More


Transformation, convolution, and correlation

Bernhard Blümich

in NMR Imaging of Materials

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198526766
eISBN:
9780191709524
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526766.003.0004
Subject:
Physics, Condensed Matter Physics / Materials

Transformation, convolution, and correlation are used over and over again in nuclear magnetic resonance (NMR) spectroscopy and imaging in different contexts and sometimes with different meanings. The ... More


Intermittent Vorticity, Power Spectral Scaling, and Dynamical Measures on Resting Brain Magnetic Field Fluctuations: A Pilot Study

Arnold J. Mandell, Karen A. Selz, Tom Holroyd, Lindsay Rutter, and Richard Coppola

in The Dynamic Brain: An Exploration of Neuronal Variability and Its Functional Significance

Published in print:
2011
Published Online:
September 2011
ISBN:
9780195393798
eISBN:
9780199897049
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195393798.003.0014
Subject:
Neuroscience, Behavioral Neuroscience, Development

A new time-dependent global MEG variable, symmetric sensor difference series, from frontal, central, parietal and temporal sensor pairs in ten task free, resting schizophrenic patients and ten age ... More


Signal Processing

Robert M. Stern, William J. Ray, and Karen S. Quigley

in Psychophysiological Recording

Published in print:
2000
Published Online:
March 2012
ISBN:
9780195113594
eISBN:
9780199846962
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195113594.003.0014
Subject:
Psychology, Health Psychology

When considering attentional abilities, two physiological variables need to be recorded: basal (tonic) activity or event-related (phasic) activity. In general, tonic activity can be derived from the ... More


Toward Automatic Recognition of Spontaneous Facial Actions

Marian Stewart Bartlett, Javier R. Movellan, Gwen Littlewort, Bjorn Braathen, Mark G. Frank, and Terrence J. Sejnowski

in What the Face Reveals: Basic and Applied Studies of Spontaneous Expression Using the Facial Action Coding System (FACS)

Published in print:
2005
Published Online:
March 2012
ISBN:
9780195179644
eISBN:
9780199847044
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195179644.003.0019
Subject:
Psychology, Cognitive Psychology

This chapter presents an approach for developing a fully automatic Facial Action Coding System (FACS). The approach uses state-of-the-art machine learning techniques that can be applied to ... More


Diffraction of Light from Blood Cells

Robert N. Compton and Michael A. Duncan

in Laser Experiments for Chemistry and Physics

Published in print:
2015
Published Online:
December 2015
ISBN:
9780198742975
eISBN:
9780191816932
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198742975.003.0030
Subject:
Physics, Atomic, Laser, and Optical Physics

The picture on the front of this book shows the diffraction pattern from a laser beam passing through a pinhole. The experiment in this chapter uses Babinet’s principle to analyze the diffraction of ... More


Microstructures and fabrics of granites

Anne Nédélec and Jean-Luc Bouchez

in Granites: Petrology, Structure, Geological Setting, and Metallogeny

Published in print:
2015
Published Online:
April 2015
ISBN:
9780198705611
eISBN:
9780191774515
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198705611.003.0009
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

Microstructures in granitic rocks essentially concern quartz grains which deliver key indications on the conditions of deformation of these rocks (magmatic versus high- or low-temperature ... More


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