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Adaptive Methods And Parallel Computation For Partial Differential Equations
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Book Synopsis Adaptive Methods and Parallel Computation for Partial Differential Equations by :
Download or read book Adaptive Methods and Parallel Computation for Partial Differential Equations written by and published by . This book was released on 1992 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consider the adaptive solution of two-dimensional vector systems of hyperbolic and elliptic partial differential equations on shared-memory parallel computers. Hyperbolic systems are approximated by an explicit finite volume technique and solved by a recursive local mesh refinement procedure on a tree- structured grid. Local refinement of the time steps and spatial cells of a coarse base mesh is performed in regions where a refinement indicator exceeds a prescribed tolerance. Computational procedures that sequentially traverse the tree while processing solutions on each grid in parallel, that process solutions at the same tree level in parallel, and that dynamically assign processors to nodes of the tree have been developed and applied to an example. Computational results comparing a variety of heuristic processor load balancing techniques and refinement strategies are presented.
Book Synopsis Multilevel Adaptive Methods for Partial Differential Equations by : Stephen F. McCormick
Download or read book Multilevel Adaptive Methods for Partial Differential Equations written by Stephen F. McCormick and published by SIAM. This book was released on 1989-01-01 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Adaptive Methods for Partial Differential Equations by : Ivo Babushka
Download or read book Adaptive Methods for Partial Differential Equations written by Ivo Babushka and published by SIAM. This book was released on 1989-01-01 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Proceedings of the Workshop on Adaptive Computational Methods for Partial Differential Equations, Rensselaer Polytechnic Institute, October 13-15, 1988"--T.p. verso.
Book Synopsis Parallel Adaptive Techniques for Transient Partial Differential Equations by :
Download or read book Parallel Adaptive Techniques for Transient Partial Differential Equations written by and published by . This book was released on 1994 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: As scientific and engineering problems increase in complexity, there is a corresponding need to automate a greater portion of the solution process. Adaptive methods are capable of providing many of the decisions - that arise when solving problems involving partial differential equations. When automatic mesh generation, refinement and coarsening is combined with method-order variation, it is possible to construct methods having spectral convergence rates. Accuracy and solution reliability are verified by asymptotically correct estimates of discretization errors. With parallel computation becoming more widespread and necessary, it is important to consider parallel adaptive strategies. Much more difficult to parallelize than traditional algorithms, adaptive strategies necessarily require dynamic processor scheduling because of load changes introduced by periodic solution enrichment. (AN).
Book Synopsis Adaptive Computational Methods for Partial Differential Equations by : Ivo Babushka
Download or read book Adaptive Computational Methods for Partial Differential Equations written by Ivo Babushka and published by SIAM. This book was released on 1983-01-01 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: List of participants; Elliptic equations; Parabolic equations; Hyperbolic equations.
Book Synopsis Parallel Multilevel Methods by : Gerhard Zumbusch
Download or read book Parallel Multilevel Methods written by Gerhard Zumbusch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Main aspects of the efficient treatment of partial differential equations are discretisation, multilevel/multigrid solution and parallelisation. These distinct topics are covered from the historical background to modern developments. It is demonstrated how the ingredients can be put together to give an adaptive and parallel multilevel approach for the solution of elliptic boundary value problems. Error estimators and adaptive grid refinement techniques for ordinary and for sparse grid discretisations are presented. Different types of additive and multiplicative multilevel solvers are discussed with respect to parallel implementation and application to adaptive refined grids. Efficiency issues are treated both for the sequential multilevel methods and for the parallel version by hash table storage techniques. Finally, space-filling curve enumeration for parallel load balancing and processor cache efficiency are discussed.
Book Synopsis Adaptive and Parallel Computation for Transient Partial Differential Equations by :
Download or read book Adaptive and Parallel Computation for Transient Partial Differential Equations written by and published by . This book was released on 2002 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: We have studied and developed procedures for the adaptive and parallel solution of transient partial differential equations. In particular, we concentrated on (i) techniques to manage distributed data, (ii) dynamic load balancing, (iii) discontinuous Galerkin schemes for hyperbolic systems, (iv) a posteriori error estimation strategies for discontinuous Galerkin methods, and (v) generalized mesh adaptation procedures. The resulting software is being applied to problems arising in several disciplines; however, it has been most successful with compressible fluid dynamics.
Author :Mitchell Barry Luskin Publisher :Springer Science & Business Media ISBN 13 :9780387950082 Total Pages :328 pages Book Rating :4.9/5 (5 download)
Book Synopsis Parallel Solution of Partial Differential Equations by : Mitchell Barry Luskin
Download or read book Parallel Solution of Partial Differential Equations written by Mitchell Barry Luskin and published by Springer Science & Business Media. This book was released on 2000 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume are based on lectures given at the IMA workshop on the Parallel Solution of PDE during June 9-13, 1997. The numerical solution of partial differential equations has been of major importance to the development of many technologies and has been the target of much of the development of parallel computer hardware and software. Parallel computer offers the promise of greatly increased performance and the routine calculation of previously intractable problems. This volume contains papers on the development and assessment of new approximation and solution techniques that can take advantage of parallel computers. It will be of interest to applied mathematicians, computer scientists, and engineers concerned with investigating the state of the art and future directions in numerical computing. Topics include domain decomposition methods, parallel multi-grid methods, front tracking methods, sparse matrix techniques, adaptive methods, fictitious domain methods, and novel time and space discretizations. Applications discussed include fluid dynamics, radiative transfer, solid mechanics, and semiconductor simulation.
Book Synopsis Adaptive Methods for Partial Differential Equations by :
Download or read book Adaptive Methods for Partial Differential Equations written by and published by . This book was released on 1994 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Solution of Partial Differential Equations on Parallel Computers by : Are Magnus Bruaset
Download or read book Numerical Solution of Partial Differential Equations on Parallel Computers written by Are Magnus Bruaset and published by Springer Science & Business Media. This book was released on 2006-03-05 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer’s silicon test tube, there is need for precise and computable process descriptions. The scienti?c ?elds of Ma- ematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs). Formulated as such equations, physical laws can become subject to computational and analytical studies. In the computational setting, the equations can be discreti ed for ef?cient solution on a computer, leading to valuable tools for simulation of natural and man-made processes. Numerical so- tion of PDE-based mathematical models has been an important research topic over centuries, and will remain so for centuries to come. In the context of computer-based simulations, the quality of the computed results is directly connected to the model’s complexity and the number of data points used for the computations. Therefore, computational scientists tend to ?ll even the largest and most powerful computers they can get access to, either by increasing the si e of the data sets, or by introducing new model terms that make the simulations more realistic, or a combination of both. Today, many important simulation problems can not be solved by one single computer, but calls for parallel computing.
Book Synopsis Adaptive Methods for Partial Differential Equations by : United States. Army Research Office
Download or read book Adaptive Methods for Partial Differential Equations written by United States. Army Research Office and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Adaptive Methods — Algorithms, Theory and Applications by : W. Hackbusch
Download or read book Adaptive Methods — Algorithms, Theory and Applications written by W. Hackbusch and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organizes workshops on subjects concerning the algorithmical treat ment of partial differential equations. The topics are discretization methods like the finite element and finite volume method for various types of applications in structural and fluid mechanics. Particular attention is devoted to advanced solu tion techniques. th The series of such workshops was continued in 1993, January 22-24, with the 9 Kiel-Seminar on the special topic "Adaptive Methods Algorithms, Theory and Applications" at the Christian-Albrechts-University of Kiel. The seminar was attended by 76 scientists from 7 countries and 23 lectures were given. The list of topics contained general lectures on adaptivity, special discretization schemes, error estimators, space-time adaptivity, adaptive solvers, multi-grid me thods, wavelets, and parallelization. Special thanks are due to Michael Heisig, who carefully compiled the contribu tions to this volume. November 1993 Wolfgang Hackbusch Gabriel Wittum v Contents Page A. AUGE, G. LUBE, D. WEISS: Galerkin/Least-Squares-FEM and Ani- tropic Mesh Refinement. 1 P. BASTIAN, G. WmUM : Adaptive Multigrid Methods: The UG Concept. 17 R. BEINERT, D. KRONER: Finite Volume Methods with Local Mesh Alignment in 2-D. 38 T. BONK: A New Algorithm for Multi-Dimensional Adaptive Nume- cal Quadrature. 54 F.A. BORNEMANN: Adaptive Solution of One-Dimensional Scalar Conservation Laws with Convex Flux. 69 J. CANU, H. RITZDORF : Adaptive, Block-Structured Multigrid on Local Memory Machines. 84 S. DAHLKE, A. KUNaTH: Biorthogonal Wavelets and Multigrid. 99 B. ERDMANN, R.H.W. HOPPE, R.
Book Synopsis Solution of Partial Differential Equations on Vector and Parallel Computers by : James M. Ortega
Download or read book Solution of Partial Differential Equations on Vector and Parallel Computers written by James M. Ortega and published by SIAM. This book was released on 1985-09-01 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Parallelism.
Book Synopsis Adaptive methods for partial differential equations : proceedings of the Workshop on Adaptive Computational Methods for Partial Differential Equations, Rensselaer Polytechnic Institute, October 13 - 15, 1988 by : Joseph E. Flaherty
Download or read book Adaptive methods for partial differential equations : proceedings of the Workshop on Adaptive Computational Methods for Partial Differential Equations, Rensselaer Polytechnic Institute, October 13 - 15, 1988 written by Joseph E. Flaherty and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing by : David H. Bailey
Download or read book Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing written by David H. Bailey and published by SIAM. This book was released on 1995-01-01 with total page 900 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings -- Parallel Computing.
Author :Stephen F. McCormick Publisher :Society for Industrial and Applied Mathematics ISBN 13 :9780898712476 Total Pages :172 pages Book Rating :4.7/5 (124 download)
Book Synopsis Multilevel Adaptive Methods for Partial Differential Equations by : Stephen F. McCormick
Download or read book Multilevel Adaptive Methods for Partial Differential Equations written by Stephen F. McCormick and published by Society for Industrial and Applied Mathematics. This book was released on 1987-01-01 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations by : Ivo Babuska
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.
