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Parallel Adaptive Techniques For Transient Partial Differential Equations
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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 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.
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 Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Book Synopsis Adaptive Parallel Multilevel Methods for Partial Differential Equations by : Gerhard Zumbusch
Download or read book Adaptive Parallel Multilevel Methods for Partial Differential Equations written by Gerhard Zumbusch and published by . This book was released on 2001 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 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 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics contained in this volume include the reliability of computations; a posteriori error estimation; adaptive h-, p-, and r-refinement; method of lines and local refinement methods for time-dependent problems; parallel solution techniques; and applications of adaptive methods to problems in elasticity, fluid mechanics, and combustion. Issues of reliability, presented in the contributions by Babuska and Szabo', note the importance of specifying computational accuracy in relation to the idealizations of the mathematical model. Thus, one should envision a sequence of computations where the enhancements and refinements are added to the physical mode as the computational procedure is enriched. These ideas are a relatively new and important innovation in the field. The contributions of Berger and Hassanzadeh et al. discuss parallel adaptive procedures, which is another aspect of the field that has emerged since the early conferences and workshops. (KR).
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 Space-Time Methods by : Ulrich Langer
Download or read book Space-Time Methods written by Ulrich Langer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-09-23 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given on stable formulations, error estimates, adaptivity in space and time, efficient solution algorithms, parallelization of the solution pipeline, and applications in science and engineering.
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 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 Wavelet Schwarz Methods for Nonlinear Elliptic Partial Differential Equations by : Dominik Lellek
Download or read book Adaptive Wavelet Schwarz Methods for Nonlinear Elliptic Partial Differential Equations written by Dominik Lellek and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adaptive wavelet methods have recently proven to be a very powerful instrument for the numerical treatment of nonlinear partial differential equations. In many cases, these methods can be shown to converge with an optimal rate with respect to the degrees of freedom and in linear complexity. In this thesis, we couple such algorithms with nonlinear Schwarz domain decomposition techniques. With this approach, we can develop efficient parallel adaptive wavelet Schwarz methods for a class of nonlinear problems and prove their convergence and optimality. We support the theoretical findings with instructive numerical experiments. In addition, we present how these techniques can be applied to the stationary, incompressible Navier-Stokes equation. Furthermore, we couple the adaptive wavelet Schwarz methods with a Newton-type method.
Book Synopsis Recent Advances in Numerical Methods for Partial Differential Equations and Applications by : Xiaobing Feng
Download or read book Recent Advances in Numerical Methods for Partial Differential Equations and Applications written by Xiaobing Feng and published by American Mathematical Soc.. This book was released on 2002 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is derived from lectures presented at the 2001 John H. Barrett Memorial Lectures at the University of Tennessee, Knoxville. The topic was computational mathematics, focusing on parallel numerical algorithms for partial differential equations, their implementation and applications in fluid mechanics and material science. Compiled here are articles from six of nine speakers. Each of them is a leading researcher in the field of computational mathematics and its applications. A vast area that has been coming into its own over the past 15 years, computational mathematics has experienced major developments in both algorithmic advances and applications to other fields. These developments have had profound implications in mathematics, science, engineering and industry. With the aid of powerful high performance computers, numerical simulation of physical phenomena is the only feasible method for analyzing many types of important phenomena, joining experimentation and theoretical analysis as the third method of scientific investigation. The three aspects: applications, theory, and computer implementation comprise a comprehensive overview of the topic. Leading lecturers were Mary Wheeler on applications, Jinchao Xu on theory, and David Keyes on computer implementation. Following the tradition of the Barrett Lectures, these in-depth articles and expository discussions make this book a useful reference for graduate students as well as the many groups of researchers working in advanced computations, including engineering and computer scientists.
Book Synopsis Numerical Methods for Singularly Perturbed Differential Equations with Applications by :
Download or read book Numerical Methods for Singularly Perturbed Differential Equations with Applications written by and published by . This book was released on 1993 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the three-year period of this project, we conducted research on the development, analysis, and application of serial and parallel adaptive computational strategies for solving transient and steady partial differential systems. Concentrating on high-order methods and adaptive approaches that combine mesh refinement and coarsening (h-refinement, order variation (p- refinement), and occasionally, mesh motion (r-refinement), we addressed problems in combustion, materials science and compressible fluid mechanics. Special spatially-discrete finite element Galerkin methods were considered for the parallel and adaptive solution of hyperbolic conservation laws. Improved solution-limiting and error-estimation strategies increased the accuracy and efficiency of these methods which are being applied to two - and three- dimensional compressible flow problems. Adaptive techniques for dissipative systems are being applied to problems in the manufacture of ceramic composite media.
Book Synopsis Domain Decomposition Methods in Science and Engineering XXIII by : Chang-Ock Lee
Download or read book Domain Decomposition Methods in Science and Engineering XXIII written by Chang-Ock Lee and published by Springer. This book was released on 2017-03-15 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers presented at the 23rd International Conference on Domain Decomposition Methods in Science and Engineering, held on Jeju Island, Korea on July 6-10, 2015. Domain decomposition methods solve boundary value problems by splitting them into smaller boundary value problems on subdomains and iterating to coordinate the solution between adjacent subdomains. Domain decomposition methods have considerable potential for a parallelization of the finite element methods, and serve a basis for distributed, parallel computations.
Book Synopsis Fluid-Structure Interaction by : Hans-Joachim Bungartz
Download or read book Fluid-Structure Interaction written by Hans-Joachim Bungartz and published by Springer Science & Business Media. This book was released on 2006-07-28 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume in the series Lecture Notes in Computational Science and Engineering presents a collection of papers presented at the International Workshop on FSI, held in October 2005 in Hohenwart and organized by DFG's Research Unit 493 "FSI: Modeling, Simulation, and Optimization". The papers address partitioned and monolithic coupling approaches, methodical issues and applications, and discuss FSI from the mathematical, informatics, and engineering points of view.
