A Mesh Moving Technique For Time Dependent Partial Differential Equations In Two Space Dimensions
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A Mesh Moving Technique For Time Dependent Partial Differential Equations In Two Space Dimensions
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Author : David C. Arney
language : en
Publisher:
Release Date : 198?
A Mesh Moving Technique For Time Dependent Partial Differential Equations In Two Space Dimensions written by David C. Arney and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 198? with Boundary value problems categories.
This article discusses an adaptive mesh moving technique that can be used with a finite difference or finite element scheme to solve initial-boundary value problems for vector systems of partial differential equations in two space dimensions and time. The mesh moving technique is based on an algebraic node movement function determined from the propagation of significant error regions. The algorithms is designed to be flexible, so that it can be used with many existing finite difference and finite element methods. To test the mesh moving algorithm, the authors implemented it in a system code with an initial mesh generator and a MacCormack finite volume scheme on quadralateral cells for hyperbolic vector systems. Results are presented for several computational examples. The moving mesh scheme reduces dispersion errors near shocks and wave fronts and thereby reduces the grid requirements necessary to compute accurate solutions while increasing computational efficiency.
A Two Dimensional Mesh Moving Technique For Time Dependent Partial Differential Equations
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Author : D. C. Arney
language : en
Publisher:
Release Date : 1985
A Two Dimensional Mesh Moving Technique For Time Dependent Partial Differential Equations written by D. C. Arney 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.
This document discusses an adaptive mesh moving technique that can be used with a finite difference or finite element scheme to solve initial-boundary value problems for vector systems of partial differential equations in two space dimensions. The mesh moving technique is based on an algebraic node movement function determined from the geometry and propagations of regions having significant discretization error indicators. This procedure is designed to be flexible, so that it can be used with many existing finite difference and finite element methods. To test the mesh moving algorithm, it was implemented in a system code with and initial mesh generator and a MacCormack finite difference scheme on quadrilateral cells for hyperbolic vector systems of conservation laws. Results are presented for several computational examples. The moving mesh scheme reduces dispersive errors near shocks and wave fronts and thereby reduces the grid requirements necessary to compute accurate solutions while incereasing computational efficiency. Additional keywords: Error clustering. (Author).
An Adaptive Mesh Moving And Local Refinement Method For Time Dependent Partial Differential Equations
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Author :
language : en
Publisher:
Release Date : 1990
An Adaptive Mesh Moving And Local Refinement Method For Time Dependent Partial Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
We discuss mesh-moving, static mesh regeneration, and local mesh-refinement algorithms that can be used with a finite difference or finite element scheme to solve initial boundary value problems for vector systems of time-dependent partial differential equations in two space dimensions and time. A coarse based mesh of quadrilateral cells is moved by an algebraic mesh-movement function so as to follow and isolate spatially distinct phenomena. The local mesh-refinement method recursively divides the time step and spatial cells of the moving base mesh in regions where error indicators are high until a prescribed tolerance is satisfied. The static mesh-regeneration procedure is used to create a new base mesh when the existing one becomes to distorted. The adaptive methods have been combined with a MacCormack finite difference scheme for hyperbolic systems and an error indicator based upon estimates of the local discretization error obtained by Richardson extrapolation. Results are presented for several computational examples.
An Adaptive Mesh Algorithm For Solving Systems Of Time Dependent Partial Differential Equations
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Author : David C. Arney
language : en
Publisher:
Release Date : 1985
An Adaptive Mesh Algorithm For Solving Systems Of Time Dependent Partial Differential Equations written by David C. Arney 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.
This thesis discusses and adaptive mesh algorithm that can be used with a finite difference or finite element scheme to solve initial-boundary value problems for vector systems of time dependent partial differential equations in two space dimensions. This algorithm combines the adaptive technique of mesh moving, static rezoning, and local mesh refinement. The nodes of a coarse mesh of quadrilateral cells are moved by a simple algebraic node movement function. The local mesh refinement method recursively divides cells of the moving coarse mesh within clustered regions that contain nodes with large error until a user prescribed error tolerance is satisfied. Keywords: Hyperbolic equations; Expert systems; and Computations.
An Adaptive Method With Mesh Moving And Local Mesh Refinement For Time Dependent Partial Differential Equations
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Author : David C. Arney
language : en
Publisher:
Release Date : 1988
An Adaptive Method With Mesh Moving And Local Mesh Refinement For Time Dependent Partial Differential Equations written by David C. Arney and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
The authors discuss mesh moving, static mesh regeneration, and local mesh refinement algorithms that can be used with a finite difference or finite element scheme to solve initial-boundary value problems for vector systems of time-dependent partial differential equations in two-space dimensions and time. A coarse base mesh of quadrilateral cells is moved by an algebraic mesh movement function so that it may follow and isolate spatially distinct phenomena. The local mesh refinement method recursively divides the time step and spatial cells of the moving base mesh in regions were error indicators are high until a prescribed tolerance is satisfied. The static mesh regeneration procedure is used to create a new base mesh when the existing ones become too distorted. In order to test our adaptive algorithms, the authors implemented them in a system code with an initial mesh generator, a MacCormack finite difference scheme for hyperbolic systems, and an error indicator based upon estimates of the local discretization error obtained by Richardson extrapolation. Results are presented for several computational examples. (kr).
Moving Grid Methods For Time Dependent Partial Differential Equations
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Author : P. A. Zegeling
language : en
Publisher:
Release Date : 1993
Moving Grid Methods For Time Dependent Partial Differential Equations written by P. A. Zegeling and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Differential equations, Partial categories.
A Moving Finite Element Method For Time Dependent Partial Differential Equations With Error Estimation And Refinement
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Author : S. Adjerid
language : en
Publisher:
Release Date : 1984
A Moving Finite Element Method For Time Dependent Partial Differential Equations With Error Estimation And Refinement written by S. Adjerid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.
The authors discuss a moving finite element method for solving vector systems of time dependent partial differential equations in one space dimension. The mesh is moved so as to equidistribute the spatial component of the discretization error in H1. They present a method of estimating this error by using p-hierarchic finite elements. The error estimate is also used in an adaptive mesh refinement procedure to give an algorithm that combines mesh movement and refinement. The authors discretize the partial differential equations in space using a Galerkin procedure with piecewise linear elements to approximate the solution and quadratic elements to estimate the error. A system of ordinary differential equations for mesh velocities are used to control element motions. The authors use existing software for stiff ordinary differential equations for the temporal integration of the solution, the error estimate, and the mesh motion. Computational results using a code based on this method are presented for several examples.
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 Finite Element Method
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Author : Maria do Carmo Coimbra
language : en
Publisher: CRC Press
Release Date : 2016-11-30
Moving Finite Element Method written by Maria do Carmo Coimbra and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-30 with Mathematics categories.
This book focuses on process simulation in chemical engineering with a numerical algorithm based on the moving finite element method (MFEM). It offers new tools and approaches for modeling and simulating time-dependent problems with moving fronts and with moving boundaries described by time-dependent convection-reaction-diffusion partial differential equations in one or two-dimensional space domains. It provides a comprehensive account of the development of the moving finite element method, describing and analyzing the theoretical and practical aspects of the MFEM for models in 1D, 1D+1d, and 2D space domains. Mathematical models are universal, and the book reviews successful applications of MFEM to solve engineering problems. It covers a broad range of application algorithm to engineering problems, namely on separation and reaction processes presenting and discussing relevant numerical applications of the moving finite element method derived from real-world process simulations.
A Parallel Multilevel Partition Of Unity Method For Elliptic Partial Differential Equations
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Author : Marc Alexander Schweitzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Parallel Multilevel Partition Of Unity Method For Elliptic Partial Differential Equations written by Marc Alexander Schweitzer 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.
the solution or its gradient. These new discretization techniques are promising approaches to overcome the severe problem of mesh-generation. Furthermore, the easy coupling of meshfree discretizations of continuous phenomena to dis crete particle models and the straightforward Lagrangian treatment of PDEs via these techniques make them very interesting from a practical as well as a theoretical point of view. Generally speaking, there are two different types of meshfree approaches; first, the classical particle methods [104, 105, 107, 108] and second, meshfree discretizations based on data fitting techniques [13, 39]. Traditional parti cle methods stem from physics applications like Boltzmann equations [3, 50] and are also of great interest in the mathematical modeling community since many applications nowadays require the use of molecular and atomistic mod els (for instance in semi-conductor design). Note however that these methods are Lagrangian methods; i. e. , they are based On a time-dependent formulation or conservation law and can be applied only within this context. In a particle method we use a discrete set of points to discretize the domain of interest and the solution at a certain time. The PDE is then transformed into equa tions of motion for the discrete particles such that the particles can be moved via these equations. After time discretization of the equations of motion we obtain a certain particle distribution for every time step.