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Parallel Methods For The Computation Of Approximate Solutions To Separable Elliptic Partial Differential Equations
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Book Synopsis Parallel Methods for the Computation of Approximate Solutions to Separable Elliptic Partial Differential Equations by : Joseph W. Nichols
Download or read book Parallel Methods for the Computation of Approximate Solutions to Separable Elliptic Partial Differential Equations written by Joseph W. Nichols and published by . This book was released on 2001 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Marc Alexander Schweitzer Publisher :Springer Science & Business Media ISBN 13 :3642593259 Total Pages :197 pages Book Rating :4.6/5 (425 download)
Book Synopsis A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations by : Marc Alexander Schweitzer
Download or read book A Parallel Multilevel Partition of Unity Method for Elliptic Partial Differential Equations written by Marc Alexander Schweitzer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: the solution or its gradient. These new discretization techniques are promising approaches to overcome the severe problem of mesh-generation. Furthermore, the easy coupling of meshfree discretizations of continuous phenomena to dis crete particle models and the straightforward Lagrangian treatment of PDEs via these techniques make them very interesting from a practical as well as a theoretical point of view. Generally speaking, there are two different types of meshfree approaches; first, the classical particle methods [104, 105, 107, 108] and second, meshfree discretizations based on data fitting techniques [13, 39]. Traditional parti cle methods stem from physics applications like Boltzmann equations [3, 50] and are also of great interest in the mathematical modeling community since many applications nowadays require the use of molecular and atomistic mod els (for instance in semi-conductor design). Note however that these methods are Lagrangian methods; i. e. , they are based On a time-dependent formulation or conservation law and can be applied only within this context. In a particle method we use a discrete set of points to discretize the domain of interest and the solution at a certain time. The PDE is then transformed into equa tions of motion for the discrete particles such that the particles can be moved via these equations. After time discretization of the equations of motion we obtain a certain particle distribution for every time step.
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 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 Some Methods for the Parallel Computation of Elliptic Partial Differential Equations by : C. C. Christara
Download or read book Some Methods for the Parallel Computation of Elliptic Partial Differential Equations written by C. C. Christara and published by . This book was released on 1991 with total page 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 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 Parallel Processing for Scientific Computing by : G. Rodrigue
Download or read book Parallel Processing for Scientific Computing written by G. Rodrigue and published by SIAM. This book was released on 1989-01-01 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Parallelism.
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 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 Numerical Methods for Partial Differential Equations by : William F. Ames
Download or read book Numerical Methods for Partial Differential Equations written by William F. Ames and published by . This book was released on 1970 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations by : Mitsuhiro T. Nakao
Download or read book Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations written by Mitsuhiro T. Nakao and published by Springer Nature. This book was released on 2019-11-11 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.
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 MUItigriD Software for Elliptic Partial Differential Equations by : John C. Adams
Download or read book MUItigriD Software for Elliptic Partial Differential Equations written by John C. Adams and published by . This book was released on 1991 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computer Methods for Partial Differential Equations: Elliptic equations and the finite-element method by : Robert Vichnevetsky
Download or read book Computer Methods for Partial Differential Equations: Elliptic equations and the finite-element method written by Robert Vichnevetsky and published by Prentice Hall. This book was released on 1981 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Parallel Iterative Techniques for the Solution of Elliptic Partial Differential Equations by : John Paul Bonomo
Download or read book Parallel Iterative Techniques for the Solution of Elliptic Partial Differential Equations written by John Paul Bonomo and published by . This book was released on 1990 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
