Moving Mesh Methods For Solving Parabolic Partial Differential Equations
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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.
Moving Mesh Methods For Non Linear Parabolic Partial Differential Equations
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Author : Kenneth William Blake
language : en
Publisher:
Release Date : 2001
Moving Mesh Methods For Non Linear Parabolic Partial Differential Equations written by Kenneth William Blake and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
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 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.
The Role Of Initial Value Solvers In A Moving Mesh Method
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Author : Linda Ju
language : en
Publisher:
Release Date : 2007
The Role Of Initial Value Solvers In A Moving Mesh Method written by Linda Ju and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Differential-algebraic equations categories.
This thesis investigates the role of different initial value solvers in moving mesh software for solving second-order parabolic partial differential equations. We confine our attention primarily to the effect of the implicit ODE solver DDASSL used in the software MOVCOL of Huang and Russell, which is based on a moving collocation method. The advantages and limitations of Backward Differentiation Formula (BDF) methods and Implicit Runge-Kutta (IRK) methods are discussed in this particular context and the alternative ODE solver PSIDE, which is based on a four-stage RADAU IIA algorithm, is examined. The new interface of PSIDE with MOVCOL is discussed in some detail. Its performance is compared with DDASSL for several numerical problems.
A Moving Mesh Finite Element Method With Local Refinement For Parabolic Partial Differential Equations
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Author : Slimane Adjerid
language : en
Publisher:
Release Date : 1985
A Moving Mesh Finite Element Method With Local Refinement For Parabolic Partial Differential Equations written by Slimane Adjerid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
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.
Adaptive Moving Mesh Methods For Partial Differential Equations
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Author : Kelsey Luisa DiPietro
language : en
Publisher:
Release Date : 2019
Adaptive Moving Mesh Methods For Partial Differential Equations written by Kelsey Luisa DiPietro and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
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
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.