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EBookClubs

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Book An Adaptive Mesh Moving and Local Refinement Method for Time Dependent Partial Differential Equations

Download or read book An Adaptive Mesh Moving and Local Refinement Method for Time Dependent Partial Differential Equations written by and published by . This book was released on 1990 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book An Adaptive Method with Mesh Moving and Local Mesh Refinement for Time Dependent Partial Differential Equations

Download or read book An Adaptive Method with Mesh Moving and Local Mesh Refinement for Time Dependent Partial Differential Equations written by David C. Arney and published by . This book was released on 1988 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Book An Adaptive Mesh Algorithm for Solving Systems of Time Dependent Partial Differential Equations

Download or read book An Adaptive Mesh Algorithm for Solving Systems of Time Dependent Partial Differential Equations written by David C. Arney and published by . This book was released on 1985 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book Adaptive Mesh Methods and Software for Time dependent Partial Differential Equations

Download or read book Adaptive Mesh Methods and Software for Time dependent Partial Differential Equations written by Shengtai Li and published by . This book was released on 1998 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Adaptive Moving Mesh Methods

Download or read book Adaptive Moving Mesh Methods written by Weizhang Huang and published by Springer Science & Business Media. This book was released on 2010-10-26 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book A Review of A Posteriori Error Estimation and Adaptive Mesh Refinement Techniques

Download or read book A Review of A Posteriori Error Estimation and Adaptive Mesh Refinement Techniques written by Rüdiger Verführt and published by Springer. This book was released on 1996-07 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations

Download or read book Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations written by Marsha J. Berger and published by . This book was released on 1982 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Book Modeling Mesh Generation and Adaptive Numerical Methods for Partial Differential Equations

Download or read book Modeling Mesh Generation and Adaptive Numerical Methods for Partial Differential Equations written by Ivo Babuska and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book Handbook of Grid Generation

Download or read book Handbook of Grid Generation written by Joe F. Thompson and published by CRC Press. This book was released on 1998-12-29 with total page 1136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Grid Generation addresses the use of grids (meshes) in the numerical solutions of partial differential equations by finite elements, finite volume, finite differences, and boundary elements. Four parts divide the chapters: structured grids, unstructured girds, surface definition, and adaption/quality. An introduction to each section provides a roadmap through the material. This handbook covers: Fundamental concepts and approaches Grid generation process Essential mathematical elements from tensor analysis and differential geometry, particularly relevant to curves and surfaces Cells of any shape - Cartesian, structured curvilinear coordinates, unstructured tetrahedra, unstructured hexahedra, or various combinations Separate grids overlaid on one another, communicating data through interpolation Moving boundaries and internal interfaces in the field Resolving gradients and controlling solution error Grid generation codes, both commercial and freeware, as well as representative and illustrative grid configurations Handbook of Grid Generation contains 37 chapters as well as contributions from more than 100 experts from around the world, comprehensively evaluating this expanding field and providing a fundamental orientation for practitioners.

Book Adaptive Mesh Strategies for the Spectral Element Method

Download or read book Adaptive Mesh Strategies for the Spectral Element Method written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1992 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Book Adaptive Mesh Experiments for Hyperbolic Partial Differential Equations

Download or read book Adaptive Mesh Experiments for Hyperbolic Partial Differential Equations written by David C. Arney and published by . This book was released on 1990 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Experiments were conducted on mesh moving and local mesh refinement algorithms that are used with a finite difference scheme to solve initial-boundary value problems for vector systems of hyperbolic partial differential equations in one dimension. The mesh moving algorithms move a coarse base mesh by a mesh movement function to follow and isolate spatially distinct phenomena. The local mesh refinement method recursively divides the time step and spatial cells in regions where error indicators are high until a prescribed error tolerance is satisfied. The adaptive mesh algorithms are implemented in a code with an initial mesh generator, a MacCormack finite difference scheme, and an error estimator. Experiments are conducted for several different problems to determine the efficiency of the adaptive methods and their combinations and to gauge their effectiveness in solving one-dimensional problems. (jhd).