Local Discontinuous Galerkin Method for Khokhlov-Zabolotskaya-Kuznetzov Equation and Improved Boussinesq Equation PDF Download
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Author: Weizhou Sun
Publisher:
ISBN:
Category :
Languages : en
Pages : 85
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Book Description
In the first part, we briefly review the discontinuous Garlerkin (DG) method and the local discontinuous Garlerkin (LDG) method. We discuss the development of those methods and explain in detail how they can be used to solve various partial differential equations. We use numerical examples to demonstrate the application of the two methods. In the second part, we develop a LDG method for Khokhlov-Zabolotskaya-Kuznet- zov (KZK) equation. L2 stability is proved for the method and several acoustic examples are studied in comparison with results of previous researchers. We show that our method produces more accurate results in some limiting cases of KZK equaiton. In the last part, an energy conserving LDG method is developed for the improved Boussinesq equation. We show that high order accuracy method can be designed. We demonstrate that optimal order accuracy can be achieved for piecewise polynomial base space and present the process we discovered the method. We also apply our algorithm to solitary waves to understand the phenomenon of the propagation of such waves.
Author: Weizhou Sun
Publisher:
ISBN:
Category :
Languages : en
Pages : 85
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Book Description
In the first part, we briefly review the discontinuous Garlerkin (DG) method and the local discontinuous Garlerkin (LDG) method. We discuss the development of those methods and explain in detail how they can be used to solve various partial differential equations. We use numerical examples to demonstrate the application of the two methods. In the second part, we develop a LDG method for Khokhlov-Zabolotskaya-Kuznet- zov (KZK) equation. L2 stability is proved for the method and several acoustic examples are studied in comparison with results of previous researchers. We show that our method produces more accurate results in some limiting cases of KZK equaiton. In the last part, an energy conserving LDG method is developed for the improved Boussinesq equation. We show that high order accuracy method can be designed. We demonstrate that optimal order accuracy can be achieved for piecewise polynomial base space and present the process we discovered the method. We also apply our algorithm to solitary waves to understand the phenomenon of the propagation of such waves.
Author: Tarek Aboelenen
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages :
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Book Description
The Ginzburg-Landau equation has been applied widely in many fields. It describes the amplitude evolution of instability waves in a large variety of dissipative systems in fluid mechanics, which are close to criticality. In this chapter, we develop a local discontinuous Galerkin method to solve the nonlinear Ginzburg-Landau equation. The nonlinear Ginzburg-Landau problem has been expressed as a system of low-order differential equations. Moreover, we prove stability and optimal order of convergence OhN+1 for Ginzburg-Landau equation where h and N are the space step size and polynomial degree, respectively. The numerical experiments confirm the theoretical results of the method.
Author: Bernardo Cockburn
Publisher:
ISBN:
Category :
Languages : en
Pages : 418
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Book Description
Author: Shukai Du
Publisher: Springer
ISBN: 9783030272296
Category : Mathematics
Languages : en
Pages : 124
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Book Description
This monograph requires basic knowledge of the variational theory of elliptic PDE and the techniques used for the analysis of the Finite Element Method. However, all the tools for the analysis of FEM (scaling arguments, finite dimensional estimates in the reference configuration, Piola transforms) are carefully introduced before being used, so that the reader does not need to go over longforgotten textbooks. Readers include: computational mathematicians, numerical analysts, engineers and scientists interested in new and computationally competitive Discontinuous Galerkin methods. The intended audience includes graduate students in computational mathematics, physics, and engineering, since the prerequisites are quite basic for a second year graduate student who has already taken a non necessarily advanced class in the Finite Element method.
Author: Eva Loch
Publisher:
ISBN:
Category :
Languages : en
Pages : 23
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Book Description
Author: Albert Cots Sarrate
Publisher:
ISBN:
Category :
Languages : en
Pages : 87
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Book Description
Author: Ben Elias
Publisher: Springer Nature
ISBN: 3030488268
Category : Mathematics
Languages : en
Pages : 588
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Book Description
This book provides a comprehensive introduction to Soergel bimodules. First introduced by Wolfgang Soergel in the early 1990s, they have since become a powerful tool in geometric representation theory. On the one hand, these bimodules are fairly elementary objects and explicit calculations are possible. On the other, they have deep connections to Lie theory and geometry. Taking these two aspects together, they offer a wonderful primer on geometric representation theory. In this book the reader is introduced to the theory through a series of lectures, which range from the basics, all the way to the latest frontiers of research. This book serves both as an introduction and as a reference guide to the theory of Soergel bimodules. Thus it is intended for anyone who wants to learn about this exciting field, from graduate students to experienced researchers.
Author: Xiaobing Feng
Publisher: Springer Science & Business Media
ISBN: 3319018183
Category : Mathematics
Languages : en
Pages : 289
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Book Description
The field of discontinuous Galerkin finite element methods has attracted considerable recent attention from scholars in the applied sciences and engineering. This volume brings together scholars working in this area, each representing a particular theme or direction of current research. Derived from the 2012 Barrett Lectures at the University of Tennessee, the papers reflect the state of the field today and point toward possibilities for future inquiry. The longer survey lectures, delivered by Franco Brezzi and Chi-Wang Shu, respectively, focus on theoretical aspects of discontinuous Galerkin methods for elliptic and evolution problems. Other papers apply DG methods to cases involving radiative transport equations, error estimates, and time-discrete higher order ALE functions, among other areas. Combining focused case studies with longer sections of expository discussion, this book will be an indispensable reference for researchers and students working with discontinuous Galerkin finite element methods and its applications.
Author: Yang-Hann Kim
Publisher: John Wiley & Sons
ISBN: 9780470825846
Category : Technology & Engineering
Languages : en
Pages : 416
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Book Description
In Sound Propagation: An Impedance Based Approach, Professor Yang-Hann Kim introduces acoustics and sound fields by using the concept of impedance. Kim starts with vibrations and waves, demonstrating how vibration can be envisaged as a kind of wave, mathematically and physically. One-dimensional waves are used to convey the fundamental concepts. Readers can then understand wave propagation in terms of characteristic and driving point impedance. The essential measures for acoustic waves, such as dB scale, octave scale, acoustic pressure, energy, and intensity, are explained. These measures are all realized by one-dimensional examples, which provide mathematically simplest but clear enough physical insights. Kim then moves on to explaining waves on a flat surface of discontinuity, demonstrating how propagation characteristics of waves change in space when there is a distributed impedance mismatch. Next is a chapter on radiation, scattering, and diffraction, where Kim shows how these topics can be explained in a unified way, by seeing the changes of waves due to spatially distributed impedance. Lastly, Kim covers sound in closed space, which is considered to be a space that is surrounded by spatially distributed impedance, and introduces two spaces: acoustically large and small space. The bulk of the book is concerned with introducing core fundamental concepts, but the appendices are included as the essentials as well to cover other important topics to extend learning. Offers a less mathematically-intensive means to understand the subject matter Provides an excellent launching point for more advanced study or for review of the basics Based on classroom tested materials developed over the course of two decades Companion site for readers, containing animations and MATLAB code downloads Videos and impedance data available from the author's website Presentation slides available for instructor use Sound Propagation is geared towards graduate students and advanced undergraduates in acoustics, audio engineering, and noise control engineering. Practicing engineers and researchers in audio engineering and noise control, or students in engineering and physics disciplines, who want to gain an understanding of sound and vibration concepts, will also find the book to be a helpful resource.
Author: John W. Weeton
Publisher:
ISBN:
Category : Chromium
Languages : en
Pages : 48
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Book Description
When compared with most alloys systems for which diffusion data have been previously obtained, the diffusion rates of chromium in alpha cobalt-chromium solid solutions were found to be low.
