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Author: Weizhang Huang
Publisher: Springer Science & Business Media
ISBN: 1441979166
Category : Mathematics
Languages : en
Pages : 446
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Book Description
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.
Author: Weizhang Huang
Publisher: Springer Science & Business Media
ISBN: 1441979166
Category : Mathematics
Languages : en
Pages : 446
Get Book Here
Book Description
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.
Author: Richard Andrew Norton
Publisher:
ISBN:
Category : Burgers equation
Languages : en
Pages : 135
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Book Description
As well as presenting the basic finite element method, this thesis presents two adaptive moving mesh methods: the moving finite element method and a class of methods based on the equidistribution principle, the so called moving mesh partial differential equations. One and two dimensional examples are given for the finite element and moving finite element methods and the one dimensional Burger's equation is successfully solved using the moving mesh partial differential equations. The code for the computer programs, written in C, that solve all the example problems is also given.
Author: Xiangmin Xu
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 0
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Book Description
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.
Author: Robert Marlow
Publisher:
ISBN:
Category :
Languages : en
Pages : 292
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Book Description
Author: Kelsey Luisa DiPietro
Publisher:
ISBN:
Category :
Languages : en
Pages : 134
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Book Description
Author: Jeremy Houston Smith
Publisher:
ISBN:
Category :
Languages : en
Pages : 434
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Book Description
Author: Ruo Li
Publisher:
ISBN:
Category : Harmonic maps
Languages : en
Pages : 22
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Book Description
Author: Simone Appella
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This note is part of Quality testing.
Author: Mohamed H. Mahmoud Sulman
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 0
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Book Description
Author: Viktor A. Rukavishnikov
Publisher: MDPI
ISBN: 3036503765
Category : Mathematics
Languages : en
Pages : 128
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Book Description
Mathematical models of various natural processes are described by differential equations, systems of partial differential equations and integral equations. In most cases, the exact solution to such problems cannot be determined; therefore, one has to use grid methods to calculate an approximate solution using high-performance computing systems. These methods include the finite element method, the finite difference method, the finite volume method and combined methods. In this Special Issue, we bring to your attention works on theoretical studies of grid methods for approximation, stability and convergence, as well as the results of numerical experiments confirming the effectiveness of the developed methods. Of particular interest are new methods for solving boundary value problems with singularities, the complex geometry of the domain boundary and nonlinear equations. A part of the articles is devoted to the analysis of numerical methods developed for calculating mathematical models in various fields of applied science and engineering applications. As a rule, the ideas of symmetry are present in the design schemes and make the process harmonious and efficient.
