Adaptive Mesh Methods And Software For Time Dependent Partial Differential Equations
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Adaptive Mesh Methods And Software For Time Dependent Partial Differential Equations
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Author : Shengtai Li
language : en
Publisher:
Release Date : 1998
Adaptive Mesh Methods And Software For Time Dependent Partial Differential Equations written by Shengtai Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 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.
Adjoint Guided Adaptive Mesh Refinement For Hyperbolic Systems Of Equations
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Author : Brisa N. Davis
language : en
Publisher:
Release Date : 2018
Adjoint Guided Adaptive Mesh Refinement For Hyperbolic Systems Of Equations written by Brisa N. Davis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
One difficulty in developing numerical methods for time-dependent partial differential equations is the fact that solutions contain time-varying regions where much higher resolution is required than elsewhere in the domain. The open source Clawpack software implements block-structured adaptive mesh refinement to selectively refine around propagating waves in the AMRClaw and GeoClaw packages. In particular, GeoClaw is widely used for tsunami modeling, the application that motivated this work. For problems where the solution must be computed over a large domain but is only of interest in one small area (e.g. one coastal community when doing tsunami modeling, or the location of a pressure gauge when doing acoustics modeling), a method that allows identifying and refining the grid only in regions that influence this target area would significantly reduce the computational cost of finding a solution. The adaptive mesh refinement approach currently implemented in AMRClaw and GeoClaw often refines waves that will not impact the target area. To remedy this, we seek a method that enables the identification and refinement of only the waves that will influence the location of interest. In this work we show that solving the time-dependent adjoint equation and using a suitable inner product with either the forward solution, or the estimated one-step error in the forward solution, allows for a more precise refinement of the relevant waves. We present the adjoint methodology first in one space dimension for illustration and in a broad context since it could also be used in other adaptive software, and for other tsunami applications beyond adaptive mesh refinement. We then show how this adjoint method has been integrated into the adaptive mesh refinement strategy of the open source AMRClaw and GeoClaw software and present linear variable coefficient acoustics and tsunami modeling results showing that the accuracy of the solution is maintained and the computational time required is significantly reduced through the integration of the adjoint method into adaptive mesh refinement. The adjoint method is compared to adaptive mesh refinement methods already available in the AMRClaw software, and the advantages and disadvantages of using the adjoint method are discussed. Other capabilities of the adjoint method such as focusing on specific time ranges of interest, sensitivity analysis, and source impact analysis and design are also presented. The new algorithms are incorporated in Clawpack and code for the examples presented in this work is archived on Github.
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.
Numerical Time Dependent Partial Differential Equations For Scientists And Engineers
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Author : Moysey Brio
language : en
Publisher: Academic Press
Release Date : 2010-09-21
Numerical Time Dependent Partial Differential Equations For Scientists And Engineers written by Moysey Brio and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-21 with Mathematics categories.
It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations
An Adaptive Mesh Moving And Local Refinement Method For Time Dependent Partial Differential Equations
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Author : David C. Arney
language : en
Publisher:
Release Date : 1987
An Adaptive Mesh Moving And Local Refinement Method 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 1987 with categories.
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 Local Mesh Refinement Method For Time Dependent Partial Differential Equations
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Author : David C. Arney
language : en
Publisher:
Release Date : 1986
An Adaptive Local Mesh Refinement Method 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 1986 with 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.