Patched Based Methods For Adaptive Mesh Refinement Solutions Of Partial Differential Equations
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Author | : |
Publisher | : |
Total Pages | : 18 |
Release | : 1997 |
Genre | : |
ISBN | : |
Download Patched Based Methods for Adaptive Mesh Refinement Solutions of Partial Differential Equations Book in PDF, Epub and Kindle
This manuscript contains the lecture notes for a course taught from July 7th through July 11th at the 1997 Numerical Analysis Summer School sponsored by C.E.A., I.N.R.I.A., and E.D.F. The subject area was chosen to support the general theme of that year's school which is ''Multiscale Methods and Wavelets in Numerical Simulation.'' The first topic covered in these notes is a description of the problem domain. This coverage is limited to classical PDEs with a heavier emphasis on hyperbolic systems and constrained hyperbolic systems. The next topic is difference schemes. These schemes are the foundation for the adaptive methods. After the background material is covered, attention is focused on a simple patched based adaptive algorithm and its associated data structures for square grids and hyperbolic conservation laws. Embellishments include curvilinear meshes, embedded boundary and overset meshes. Next, several strategies for parallel implementations are examined. The remainder of the notes contains descriptions of elliptic solutions on the mesh hierarchy, elliptically constrained flow solution methods and elliptically constrained flow solution methods with diffusion.
Author | : Tomasz Plewa |
Publisher | : Springer Science & Business Media |
Total Pages | : 550 |
Release | : 2005-12-20 |
Genre | : Mathematics |
ISBN | : 3540270396 |
Download Adaptive Mesh Refinement - Theory and Applications Book in PDF, Epub and Kindle
Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models and equations used in these disciplines are rather different, yet algorithmic and implementation issues facing practitioners are often remarkably similar. Unfortunately, there has been little effort to review the advances and outstanding issues of adaptive mesh refinement methods across such a variety of fields. This book attempts to bridge this gap. The book presents a collection of papers by experts in the field of AMR who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing.
Author | : Shengtai Li |
Publisher | : |
Total Pages | : 574 |
Release | : 1998 |
Genre | : |
ISBN | : |
Download Adaptive Mesh Methods and Software for Time-dependent Partial Differential Equations Book in PDF, Epub and Kindle
Author | : Marsha J. Berger |
Publisher | : |
Total Pages | : 236 |
Release | : 1982 |
Genre | : Difference equations |
ISBN | : |
Download Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations Book in PDF, Epub and Kindle
The authors present an adaptive method based on the idea of multiple, component grids for the solution of hyperbolic partial differential equations using finite difference techniques. Based upon Richardson-type estimates of the truncation error, refined grids are created or existing ones removed to attain a given accuracy for a minimum amount of work. Their approach is recursive in that fine grids can themselves contain even finer grids. The grids with finer mesh width in space also have a smaller mesh width in time, making this a mesh refinement algorithm in time and space. This document includes algorithm, data structures and grid generation procedure, and concludes with numerical examples in one and two space dimensions. (Author).
Author | : Stanford University. Computer Science Department. Numerical Analysis Project |
Publisher | : |
Total Pages | : 55 |
Release | : 1983 |
Genre | : |
ISBN | : |
Download Adaptive mesh refinement for hyperbolic partial differential equations Book in PDF, Epub and Kindle
The authors present an adaptive method based on the idea of multiple, component grids for the solution of hyperbolic partial differential equations using finite difference techniques. Based upon Richardson-type estimates of the truncation error, refined grids are created or existing ones removed to attain a given accuracy for a minimum amount of work. Their approach is recursive in that fine grids can themselves contain even finer grids. The grids with finer mesh width in space also have a smaller mesh width in time, making this a mesh refinement algorithm in time and space. This document includes algorithm, data structures and grid generation procedure, and concludes with numerical examples in one and two space dimensions. (Author).
Author | : Stephen F. McCormick |
Publisher | : SIAM |
Total Pages | : 171 |
Release | : 1989-01-01 |
Genre | : Mathematics |
ISBN | : 9781611971026 |
Download Multilevel Adaptive Methods for Partial Differential Equations Book in PDF, Epub and Kindle
A practical handbook for understanding and using fast adaptive composite grid (FAC) methods for discretization and solution of partial differential equations (PDEs). Contains fundamental concepts. These so-called FAC are characterized by their use of a composite grid, which is nominally the union of various uniform grids. FAC is capable of producing a composite grid with tailored resolution, and a corresponding solution with commensurate accuracy, at a cost proportional to the number of composite grid points. Moreover, special asynchronous versions of the fast adaptive composite grid methods (AFAC) studied here have seemingly optimal complexity in a parallel computing environment. Most of the methods treated in this book were discovered only within the last decade, and in many cases their development is still in its infancy. While this is not meant to be comprehensive, it does provide a theoretical and practical guide to multilevel adaptive methods and relevant discretization techniques. It also contains new material, which is included to fill in certain gaps and to expose new avenues of research. Also, because adaptive refinement seems to demand a lot of attention to philosophical issues, personal perspectives are often brought freely into the discussion.
Author | : Institute for Computer Applications in Science and Engineering |
Publisher | : |
Total Pages | : 28 |
Release | : 1992 |
Genre | : |
ISBN | : |
Download Adaptive Mesh Strategies for the Spectral Element Method Book in PDF, Epub and Kindle
An adaptive spectral element method has been developed for the efficient solution of time dependent partial differential equations. Adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the one-dimensional viscous Burgers equation and the two-dimensional Navier-Stokes equations for driven flow in a cavity. Sharp gradients, singularities and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate the choice of refinement to be used. The adaptive formulation presents significant increases in efficiency, flexibility and general capabilities for high order spectral methods.
Author | : Shen Lu |
Publisher | : |
Total Pages | : 124 |
Release | : 1991 |
Genre | : |
ISBN | : |
Download An Adaptive Local Mesh Refinement Method for Solving Time Dependent Partial Differential Equations Book in PDF, Epub and Kindle
Author | : Ivo Babushka |
Publisher | : SIAM |
Total Pages | : 382 |
Release | : 1989-01-01 |
Genre | : Mathematics |
ISBN | : 9780898712421 |
Download Adaptive Methods for Partial Differential Equations Book in PDF, Epub and Kindle
"Proceedings of the Workshop on Adaptive Computational Methods for Partial Differential Equations, Rensselaer Polytechnic Institute, October 13-15, 1988"--T.p. verso.
Author | : Ivo Babuska |
Publisher | : Springer Science & Business Media |
Total Pages | : 487 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461242487 |
Download Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations Book in PDF, Epub and Kindle
With considerations such as complex-dimensional geometries and nonlinearity, the computational solution of partial differential systems has become so involved that it is important to automate decisions that have been normally left to the individual. This book covers such decisions: 1) mesh generation with links to the software generating the domain geometry, 2) solution accuracy and reliability with mesh selection linked to solution generation. This book is suited for mathematicians, computer scientists and engineers and is intended to encourage interdisciplinary interaction between the diverse groups.