Application Of Moving Mesh Methods For The Solution Of Partial Differential Equations
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Application Of Moving Mesh Methods For The Solution Of Partial Differential Equations
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Author : Simone Appella
language : en
Publisher:
Release Date : 2023
Application Of Moving Mesh Methods For The Solution Of Partial Differential Equations written by Simone Appella and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.
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Adaptive Moving Mesh Methods
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Author : Weizhang Huang
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-26
Adaptive Moving Mesh Methods written by Weizhang Huang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-26 with Mathematics categories.
This book is about adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations. It presents a general framework and theory for adaptive mesh generation and gives a comprehensive treatment of moving mesh methods and their basic components, along with their application for a number of nontrivial physical problems. Many explicit examples with computed figures illustrate the various methods and the effects of parameter choices for those methods. Graduate students, researchers and practitioners working in this area will benefit from this book.
Moving Mesh Methods For Moving Boundary Problems And Higher Order Partial Differential Equations
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Author : Xiangmin Xu
language : en
Publisher:
Release Date : 2008
Moving Mesh Methods For Moving Boundary Problems And Higher Order Partial Differential Equations written by Xiangmin Xu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Boundary value problems categories.
This thesis studies the moving mesh method and its applications in the numerical solution of moving boundary problems and higher order evolutionary partial differential equations. The concept of equidistribution has played a fundamental role in moving mesh methods. For a given adaptation function, de Boor's algorithm is commonly used for generating equidistributing meshes. The algorithm produces a sequence of meshes upon using piecewise constant interpolation for the adaptation function on the current mesh and generating a new mesh that exactly equidistributes the interpolant. Although the effectiveness of this algorithm was confirmed numerically long ago, the proof for the existence of the limit mesh and the convergence of this algorithm have thus far remained theoretically elusive. These theoretical issues are treated in Chapter 2 of this thesis. Numerical results are also given to illustrate the theoretical findings as well as stopping criteria necessary for the implementation of the algorithm. The use of moving meshes has become a popular technique for improving existing approximation schemes for moving boundary problems. In Chapter 3, we study the relative efficiency and accuracy of various numerical methods for moving boundary problems on moving meshes. A moving mesh front-tracking method based on equidistributing a specially designed adaptation function is proposed for moving boundary problems of implicit type. The resulting numerical method does not require any analytical knowledge of solutions, assumptions on solution profiles or interpolation/extrapolation which are common in other methods in the literature. Some preliminary work for moving mesh front-tracking methods in two dimensions is presented in Chapter 4. Finally, MOVCOL4, a moving mesh collocation code specifically designed for solving general fourth-order evolutionary partial differential equations, is analyzed in Chapter 5.
Partial Differential Equations
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Author : D. Sloan
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Partial Differential Equations written by D. Sloan and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight into the underlying stability and accuracy properties of computational algorithms for PDEs was deepened by building upon recent progress in mathematical analysis and in the theory of PDEs. To embark on a comprehensive review of the field of numerical analysis of partial differential equations within a single volume of this journal would have been an impossible task. Indeed, the 16 contributions included here, by some of the foremost world authorities in the subject, represent only a small sample of the major developments. We hope that these articles will, nevertheless, provide the reader with a stimulating glimpse into this diverse, exciting and important field. The opening paper by Thomée reviews the history of numerical analysis of PDEs, starting with the 1928 paper by Courant, Friedrichs and Lewy on the solution of problems of mathematical physics by means of finite differences. This excellent survey takes the reader through the development of finite differences for elliptic problems from the 1930s, and the intense study of finite differences for general initial value problems during the 1950s and 1960s. The formulation of the concept of stability is explored in the Lax equivalence theorem and the Kreiss matrix lemmas. Reference is made to the introduction of the finite element method by structural engineers, and a description is given of the subsequent development and mathematical analysis of the finite element method with piecewise polynomial approximating functions. The penultimate section of Thomée's survey deals with `other classes of approximation methods', and this covers methods such as collocation methods, spectral methods, finite volume methods and boundary integral methods. The final section is devoted to numerical linear algebra for elliptic problems. The next three papers, by Bialecki and Fairweather, Hesthaven and Gottlieb and Dahmen, describe, respectively, spline collocation methods, spectral methods and wavelet methods. The work by Bialecki and Fairweather is a comprehensive overview of orthogonal spline collocation from its first appearance to the latest mathematical developments and applications. The emphasis throughout is on problems in two space dimensions. The paper by Hesthaven and Gottlieb presents a review of Fourier and Chebyshev pseudospectral methods for the solution of hyperbolic PDEs. Particular emphasis is placed on the treatment of boundaries, stability of time discretisations, treatment of non-smooth solutions and multidomain techniques. The paper gives a clear view of the advances that have been made over the last decade in solving hyperbolic problems by means of spectral methods, but it shows that many critical issues remain open. The paper by Dahmen reviews the recent rapid growth in the use of wavelet methods for PDEs. The author focuses on the use of adaptivity, where significant successes have recently been achieved. He describes the potential weaknesses of wavelet methods as well as the perceived strengths, thus giving a balanced view that should encourage the study of wavelet methods.
Meshfree Methods For Partial Differential Equations
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Author : Michael Griebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Meshfree Methods For Partial Differential Equations written by Michael Griebel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models are often better suited to cope with geometric changes of the domain of interest, e.g. free surfaces and large deformations, than classical discretization techniques such as finite differences, finite elements or finite volumes. Another obvious advantage of meshfree discretizations is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDEs from a Lagrangian point of view and the coupling of particle models and continuous models gained enormous interest in recent years from a theoretical as well as from a practial point of view. This volume consists of articles which address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM etc.) and their application in applied mathematics, physics and engineering.
Adaptive Moving Mesh Methods
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Author : Weizhang Huang
language : en
Publisher: Springer
Release Date : 2010-10-26
Adaptive Moving Mesh Methods written by Weizhang Huang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-26 with Mathematics categories.
This book is about adaptive mesh generation and moving mesh methods for the numerical solution of time-dependent partial differential equations. It presents a general framework and theory for adaptive mesh generation and gives a comprehensive treatment of moving mesh methods and their basic components, along with their application for a number of nontrivial physical problems. Many explicit examples with computed figures illustrate the various methods and the effects of parameter choices for those methods. Graduate students, researchers and practitioners working in this area will benefit from this book.
Meshfree Methods For Partial Differential Equations Iii
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Author : Michael Griebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-18
Meshfree Methods For Partial Differential Equations Iii written by Michael Griebel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-18 with Mathematics categories.
Meshfree methods for the numerical solution of partial differential equations are becoming more and more mainstream in many areas of applications. This volume represents the state-of-the-art in meshfree methods. It consists of articles which address the different meshfree techniques, their mathematical properties and their application in applied mathematics, physics and engineering.
Moving Mesh Methods For Solving Partial Differential Equations
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Author : Robert Marlow
language : en
Publisher:
Release Date : 2010
Moving Mesh Methods For Solving Partial Differential Equations written by Robert Marlow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
Meshfree Methods For Partial Differential Equations Ii
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Author : Michael Griebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-21
Meshfree Methods For Partial Differential Equations Ii written by Michael Griebel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-21 with Mathematics categories.
The numerical treatment of partial differential equations with particle methods and meshfree discretization techniques is a very active research field both in the mathematics and engineering community. Due to their independence of a mesh, particle schemes and meshfree methods can deal with large geometric changes of the domain more easily than classical discretization techniques. Furthermore, meshfree methods offer a promising approach for the coupling of particle models to continuous models. This volume of LNCSE is a collection of the papers from the proceedings of the Second International Workshop on Meshfree Methods held in September 2003 in Bonn. The articles address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM, etc.) and their application in applied mathematics, physics and engineering. The volume is intended to foster this new and exciting area of interdisciplinary research and to present recent advances and results in this field.
Moving Mesh Methods For Solving Parabolic Partial Differential Equations
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Author : Robert Marlow
language : en
Publisher:
Release Date : 2010
Moving Mesh Methods For Solving Parabolic Partial Differential Equations written by Robert Marlow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
In this thesis, we introduce and assess a new adaptive method for solving non-linear parabolic partial differential equations with fixed or moving boundaries, using a moving mesh with continuous finite elements. The evolution of the mesh within the interior of the spatial domain is based upon conserving the distribution of a chosen monitor function across the domain throughout time, where the initial distribution is based upon the given initial data. For the moving boundary cases, the mesh movement at the boundary is governed by a second monitor function. The method is applied with different monitor functions, to the semilinear heat equation in one space dimension, and the porous medium equation in one and two space dimensions. The effects of optimising initial data for chosen monitors will be considered - in these cases, maintaining the initial distribution amounts to equidistribution. A quantification of the effects of a mesh moving away from an equidistribution are considered here, also the effects of tangling, and then untangling a mesh and restarting.