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Numerical Solution Of Partial Differential Equations On Parallel Computers
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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 Solving Partial Differential Equations on Parallel Computers by : Jianping Zhu
Download or read book Solving Partial Differential Equations on Parallel Computers written by Jianping Zhu and published by World Scientific. This book was released on 1994 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory book on supercomputer applications written by a researcher who is working on solving scientific and engineering application problems on parallel computers. The book is intended to quickly bring researchers and graduate students working on numerical solutions of partial differential equations with various applications into the area of parallel processing.The book starts from the basic concepts of parallel processing, like speedup, efficiency and different parallel architectures, then introduces the most frequently used algorithms for solving PDEs on parallel computers, with practical examples. Finally, it discusses more advanced topics, including different scalability metrics, parallel time stepping algorithms and new architectures and heterogeneous computing networks which have emerged in the last few years of high performance computing. Hundreds of references are also included in the book to direct interested readers to more detailed and in-depth discussions of specific topics.
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 Models for Parallel and Distributed Computation by : R. Correa
Download or read book Models for Parallel and Distributed Computation written by R. Correa and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parallel and distributed computation has been gaining a great lot of attention in the last decades. During this period, the advances attained in computing and communication technologies, and the reduction in the costs of those technolo gies, played a central role in the rapid growth of the interest in the use of parallel and distributed computation in a number of areas of engineering and sciences. Many actual applications have been successfully implemented in various plat forms varying from pure shared-memory to totally distributed models, passing through hybrid approaches such as distributed-shared memory architectures. Parallel and distributed computation differs from dassical sequential compu tation in some of the following major aspects: the number of processing units, independent local dock for each unit, the number of memory units, and the programming model. For representing this diversity, and depending on what level we are looking at the problem, researchers have proposed some models to abstract the main characteristics or parameters (physical components or logical mechanisms) of parallel computers. The problem of establishing a suitable model is to find a reasonable trade-off among simplicity, power of expression and universality. Then, be able to study and analyze more precisely the behavior of parallel applications.
Author :Hans Petter Langtangen Publisher :Springer Science & Business Media ISBN 13 :3642182372 Total Pages :676 pages Book Rating :4.6/5 (421 download)
Book Synopsis Advanced Topics in Computational Partial Differential Equations by : Hans Petter Langtangen
Download or read book Advanced Topics in Computational Partial Differential Equations written by Hans Petter Langtangen and published by Springer Science & Business Media. This book was released on 2012-09-22 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: A gentle introduction to advanced topics such as parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to ‘compute’ solutions to problems, hence algorithmic and software issues play a central role. All software examples use the Diffpack programming environment - some experience with Diffpack is required. There are also some chapters covering complete applications, i.e., the way from a model, expressed as systems of PDEs, through to discretization methods, algorithms, software design, verification, and computational examples. Suitable for readers with a background in basic finite element and finite difference methods for partial differential equations.
Book Synopsis Parallel Solution of Partial Differential Equations by : Petter Bjorstad
Download or read book Parallel Solution of Partial Differential Equations written by Petter Bjorstad and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications PARALLEL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS is based on the proceedings of a workshop with the same title. The work shop was an integral part of the 1996-97IMA program on "MATHEMAT ICS IN HIGH-PERFORMANCE COMPUTING." I would like to thank Petter Bj0rstad of the Institutt for Informatikk, University of Bergen and Mitchell Luskin of the School of Mathematics, University of Minnesota for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Founda tion (NSF), Department of Energy (DOE), and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr., Professor and Director v PREFACE 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 computers offer the promise of greatly increased perfor mance and the routine calculation of previously intractable problems. The papers in this volume were presented at the IMA workshop on the Paral lel Solution of PDE held during June 9-13, 1997. The workshop brought together leading numerical analysts, computer scientists, and engineers to assess the state-of-the-art and to consider future directions.
Book Synopsis A Tutorial on Elliptic PDE Solvers and Their Parallelization by : Craig C. Douglas
Download or read book A Tutorial on Elliptic PDE Solvers and Their Parallelization written by Craig C. Douglas and published by SIAM. This book was released on 2003-01-01 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This compact yet thorough tutorial is the perfect introduction to the basic concepts of solving partial differential equations (PDEs) using parallel numerical methods. In just eight short chapters, the authors provide readers with enough basic knowledge of PDEs, discretization methods, solution techniques, parallel computers, parallel programming, and the run-time behavior of parallel algorithms to allow them to understand, develop, and implement parallel PDE solvers. Examples throughout the book are intentionally kept simple so that the parallelization strategies are not dominated by technical details.
Book Synopsis PETSc for Partial Differential Equations: Numerical Solutions in C and Python by : Ed Bueler
Download or read book PETSc for Partial Differential Equations: Numerical Solutions in C and Python written by Ed Bueler and published by SIAM. This book was released on 2020-10-22 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.
Book Synopsis Scientific Computing by : Gene H. Golub
Download or read book Scientific Computing written by Gene H. Golub and published by Elsevier. This book was released on 2014-06-28 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the basic concepts of parallel and vector computing in the context of an introduction to numerical methods. It contains chapters on parallel and vector matrix multiplication and solution of linear systems by direct and iterative methods. It is suitable for advanced undergraduate and beginning graduate courses in computer science, applied mathematics, and engineering. Ideally, students will have access to a parallel or Vector computer, but the material can be studied profitably in any case. Gives a modern overview of scientific computing including parallel an vector computation Introduces numerical methods for both ordinary and partial differential equations Has considerable discussion of both direct and iterative methods for linear systems of equations, including parallel and vector algorithms Covers most of the main topics for a first course in numerical methods and can serve as a text for this course
Book Synopsis Domain Decomposition by : Barry Smith
Download or read book Domain Decomposition written by Barry Smith and published by Cambridge University Press. This book was released on 2004-03-25 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an easy-to-read discussion of domain decomposition algorithms, their implementation and analysis. Ideal for graduate students about to embark on a career in computational science. It will also be a valuable resource for all those interested in parallel computing and numerical computational methods.
Book Synopsis Group Explicit Methods for the Numerical Solution of Partial Differential Equations by : David J. Evans
Download or read book Group Explicit Methods for the Numerical Solution of Partial Differential Equations written by David J. Evans and published by CRC Press. This book was released on 1997-05-22 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new class of methods, termed "group explicit methods," is introduced in this text. Their applications to solve parabolic, hyperbolic and elliptic equations are outlined, and the advantages for their implementation on parallel computers clearly portrayed. Also included are the introductory and fundamental concepts from which the new methods are derived, and on which they are dependent. With the increasing advent of parallel computing into all aspects of computational mathematics, there is no doubt that the new methods will be widely used.
Book Synopsis Finite Difference Computing with PDEs by : Hans Petter Langtangen
Download or read book Finite Difference Computing with PDEs written by Hans Petter Langtangen and published by Springer. This book was released on 2017-06-21 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.
Book Synopsis Algorithms for Elliptic Problems by : Marián Vajtersic
Download or read book Algorithms for Elliptic Problems written by Marián Vajtersic and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with problems of modern effective algorithms for the numerical solution of the most frequently occurring elliptic partial differential equations. From the point of view of implementation, attention is paid to algorithms for both classical sequential and parallel computer systems. The first two chapters are devoted to fast algorithms for solving the Poisson and biharmonic equation. In the third chapter, parallel algorithms for model parallel computer systems of the SIMD and MIMD types are described. The implementation aspects of parallel algorithms for solving model elliptic boundary value problems are outlined for systems with matrix, pipeline and multiprocessor parallel computer architectures. A modern and popular multigrid computational principle which offers a good opportunity for a parallel realization is described in the next chapter. More parallel variants based in this idea are presented, whereby methods and assignments strategies for hypercube systems are treated in more detail. The last chapter presents VLSI designs for solving special tridiagonal linear systems of equations arising from finite-difference approximations of elliptic problems. For researchers interested in the development and application of fast algorithms for solving elliptic partial differential equations using advanced computer systems.
Book Synopsis Parallel and Sequential Methods for Ordinary Differential Equations by : Kevin Burrage
Download or read book Parallel and Sequential Methods for Ordinary Differential Equations written by Kevin Burrage and published by . This book was released on 1995 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Parallel Computing by : Roman Trobec
Download or read book Parallel Computing written by Roman Trobec and published by Springer Science & Business Media. This book was released on 2009-06-18 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of parallel programming and architectures is essential for simulating and solving problems in modern computational practice. There has been rapid progress in microprocessor architecture, interconnection technology and software devel- ment, which are in?uencing directly the rapid growth of parallel and distributed computing. However, in order to make these bene?ts usable in practice, this dev- opment must be accompanied by progress in the design, analysis and application aspects of parallel algorithms. In particular, new approaches from parallel num- ics are important for solving complex computational problems on parallel and/or distributed systems. The contributions to this book are focused on topics most concerned in the trends of today’s parallel computing. These range from parallel algorithmics, progr- ming, tools, network computing to future parallel computing. Particular attention is paid to parallel numerics: linear algebra, differential equations, numerical integ- tion, number theory and their applications in computer simulations, which together form the kernel of the monograph. We expect that the book will be of interest to scientists working on parallel computing, doctoral students, teachers, engineers and mathematicians dealing with numerical applications and computer simulations of natural phenomena.
Book Synopsis Numerical Solution of Partial Differential Equations by : Gordon D. Smith
Download or read book Numerical Solution of Partial Differential Equations written by Gordon D. Smith and published by Oxford University Press. This book was released on 1985 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.
Book Synopsis Numerical Solution of Partial Differential Equations by the Finite Element Method by : Claes Johnson
Download or read book Numerical Solution of Partial Differential Equations by the Finite Element Method written by Claes Johnson and published by Courier Corporation. This book was released on 2012-05-23 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.
