A Wavelet-Optimized, Very High Order Adaptive Grid and Order Numerical Method PDF Download
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Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781722040642
Category :
Languages : en
Pages : 48
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Book Description
Differencing operators of arbitrarily high order can be constructed by interpolating a polynomial through a set of data followed by differentiation of this polynomial and finally evaluation of the polynomial at the point where a derivative approximation is desired. Furthermore, the interpolating polynomial can be constructed from algebraic, trigonometric, or, perhaps exponential polynomials. This paper begins with a comparison of such differencing operator construction. Next, the issue of proper grids for high order polynomials is addressed. Finally, an adaptive numerical method is introduced which adapts the numerical grid and the order of the differencing operator depending on the data. The numerical grid adaptation is performed on a Chebyshev grid. That is, at each level of refinement the grid is a Chebvshev grid and this grid is refined locally based on wavelet analysis. Jameson, Leland Langley Research Center NAS1-19480; RTOP 505-90-52-01...
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
ISBN: 9781722040642
Category :
Languages : en
Pages : 48
Get Book Here
Book Description
Differencing operators of arbitrarily high order can be constructed by interpolating a polynomial through a set of data followed by differentiation of this polynomial and finally evaluation of the polynomial at the point where a derivative approximation is desired. Furthermore, the interpolating polynomial can be constructed from algebraic, trigonometric, or, perhaps exponential polynomials. This paper begins with a comparison of such differencing operator construction. Next, the issue of proper grids for high order polynomials is addressed. Finally, an adaptive numerical method is introduced which adapts the numerical grid and the order of the differencing operator depending on the data. The numerical grid adaptation is performed on a Chebyshev grid. That is, at each level of refinement the grid is a Chebvshev grid and this grid is refined locally based on wavelet analysis. Jameson, Leland Langley Research Center NAS1-19480; RTOP 505-90-52-01...
Author: Leland M. Jameson
Publisher:
ISBN:
Category : Numerical grid generation (Numerical analysis)
Languages : en
Pages : 48
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Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Constructing numerical schemes which are both adaptive and suitable for parallel architectures is very challenging. The challenge lies in the need to maintain a balanced load across the processing elements using a method that is both efficient and scalable. Here we propose a method which is adaptive, load balanced, absolutely efficient and scalable offering significant speedup over lower order adaptive schemes. The ability of wavelets to accurately and efficiently represent functions with localized features has spawned intensive research into applying wavelets for the solution of partial differential equations with the promise of significantly reducing the necessary computational effort and memory requirements. Traditionally, this effort has been centered around using wavelets as an orthogonal and complete basis, spanning a space in which to seek approximate solutions satisfying the equation in a Galerkin sense. Besides from the well known difficulties associated with such an approach for non-linear problems, one is also faced with the problem of dealing with non-trivial boundary conditions in an accurate and stable manner. Such restrictions on the applicability of wavelet based methods for the solution of problems of more general interest have, in recent years, induced significant interest into grid-based collocation wavelet methods, with various different approaches being taken. The formulation and implementation of multi-dimensional pure wavelet collocation methods, however, remains a challenging task and many issues require attention. In the present work we take a somewhat different approach to arrive at a grid based method utilizing the unique properties of wavelets. Rather than using the wavelets as a basis, we utilize the ability of wavelets to not only detect the existence of high-frequency information but also to supply information about the spatial location of such strongly inhomogeneous regions.
Author: Mani Mehra
Publisher: Springer
ISBN: 9811325952
Category : Mathematics
Languages : en
Pages : 185
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Book Description
This 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.
Author: J. S. Hesthaven
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 24
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Book Description
Author: Tian-Xiao He
Publisher: CRC Press
ISBN: 9780824704179
Category : Mathematics
Languages : en
Pages : 446
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Book Description
This volume contains papers selected from the Wavelet Analysis and Multiresolution Methods Session of the AMS meeting held at the University of Illinois at Urbana-Champaign. The contributions cover: construction, analysis, computation and application of multiwavelets; scaling vectors; nonhomogenous refinement; mulivariate orthogonal and biorthogonal wavelets; and other related topics.
Author: Mei Kobayashi
Publisher: SIAM
ISBN: 0898714168
Category : Mathematics
Languages : en
Pages : 155
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Book Description
This collection of independent case studies demonstrates how wavelet techniques have been used to solve open problems and develop insight into the nature of the systems under study. Each case begins with a description of the problem and points to the specific properties of wavelets and techniques used for determining a solution. The cases range from a very simple wavelet-based technique for reducing noise in laboratory data to complex work on two-dimensional geographical data display conducted at the Earthquake Research Institute in Japan. One case study shows how wavelet analysis is used in the development of a Japanese text-to-speech system for personal computers and another presents new wavelet techniques developed for and applied to the study of atmospheric wind, turbulent fluid, and seismic acceleration data.
Author: Ülo Lepik
Publisher: Springer Science & Business Media
ISBN: 3319042955
Category : Technology & Engineering
Languages : en
Pages : 209
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Book Description
This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems. Haar wavelet-based solutions for a wide range of problems, such as various differential and integral equations, fractional equations, optimal control theory, buckling, bending and vibrations of elastic beams are considered. Numerical examples demonstrating the efficiency and accuracy of the Haar method are provided for all solutions.
Author: Jan S. Hesthaven
Publisher:
ISBN:
Category :
Languages : en
Pages : 26
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Book Description
Author: Andrea Alberto Mammoli
Publisher: WIT Press
ISBN: 1845640306
Category : Science
Languages : en
Pages : 385
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Book Description
A common feature of multiphase flows is that a dispersed or discontinuous phase is being carried by a continuous phase, for example water drops in gas flow, solid particles in water flow, or gas bubbles in liquid flow. The overall behavior of the flow is shaped largely by the interaction between the discontinuous elements--drops, particles, bubbles
