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检索条件"丛书名=Numerical Methods and Algorithms"

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Matrix-Based Multigrid 2nd ed. 2008

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丛书名： numerical methods and algorithms

2008年

作者： Yair Shapira

ISBN: (数字)9780387497655

ISBN: (纸本)9780387497648

This book introduces and analyzes the multigrid approach for the numerical solution of large sparse linear systems arising from the discretization of elliptic partial differential equations. Special attention is given to the powerful matrix-based-multigrid approach, which is particularly useful for problems with variable coefficients and nonsymmetric and indefinite problems. This approach applies not only to model problems on rectangular grids but also to more realistic applications with complicated grids and domains and discontinuous coefficients. Matrix-Based Multigrid can be used as a textbook in courses in numerical analysis, numerical linear algebra, and numerical PDEs at the advanced undergraduate and graduate levels in computer science, math, and applied math departments. The theory is written in simple algebraic terms and therefore requires preliminary knowledge in basic linear algebra and calculus only. Because it is self contained and includes useful exercises, the book is also suitable for self study by research students, researchers, engineers, and others interested in the numerical solution of partial differential equations.

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numerical methods for Laplace Transform Inversion 2007

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丛书名： numerical methods and algorithms

2007年

作者： Alan M. Cohen

ISBN: (数字)9780387688558

ISBN: (纸本)9780387282619

Operational methods have been used for over a century to solve problems such as ordinary and partial differential equations. When solving such problems, in many cases it is fairly easy to obtain the Laplace transform, while it is very demanding to determine the inverse Laplace transform that is the solution of a given problem. Sometimes, after some difficult contour integration, we may find that a series solution results, but this may be quite difficult to evaluate in order to get an answer at a particular time value. The advent of computers has given an impetus to developing numerical methods for the determination of the inverse Laplace transform. This book gives background material on the theory of Laplace transforms, together with a fairly comprehensive list of methods that are available at the current time. Computer programs are included for those methods that perform consistently well on a wide range of Laplace transforms.

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The Schur Complement and Its Applications 2005

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丛书名： numerical methods and algorithms

2005年

作者： Fuzhen Zhang

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Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics 1

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丛书名： numerical methods and algorithms

2005年

作者： Titus Petrila Damian Trif

This handbook brings together the theoretical basics of fluid dynamics with a systemaic overview of the appropriate numerical and computational methods for solving the problems presented in the book. Also, effective c... 详细信息

ISBN: (数字)9780387238388

ISBN: (纸本)9780387238371

关键词： Fluid dynamics.

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Computational Aspects of Linear Control 1

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丛书名： numerical methods and algorithms 1

2002年

作者： Claude Brezinski (auth.) Claude Brezinski (eds.)

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Matrix-Based Multigrid 2

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丛书名： numerical methods and algorithms

1000年

作者： Yair Shapira

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Matrix-Based Multigrid 1

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丛书名： numerical methods and algorithms

1000年

作者： Yair Shapira

ISBN: (数字)9781475737264

Many important problems in applied science and engineering, such as the Navier Stokes equations in fluid dynamics, the primitive equations in global climate mod eling, the strain-stress equations in mechanics, the neutron diffusion equations in nuclear engineering, and MRIICT medical simulations, involve complicated sys tems of nonlinear partial differential equations. When discretized, such problems produce extremely large, nonlinear systems of equations, whose numerical solution is prohibitively costly in terms of time and storage. High-performance (parallel) computers and efficient (parallelizable) algorithms are clearly necessary. Three classical approaches to the solution of such systems are: Newton's method, Preconditioned Conjugate Gradients (and related Krylov-space acceleration tech niques), and multigrid methods. The first two approaches require the solution of large sparse linear systems at every iteration, which are themselves often solved by multigrid methods. Developing robust and efficient multigrid algorithms is thus of great importance. The original multigrid algorithm was developed for the Poisson equation in a square, discretized by finite differences on a uniform grid. For this model problem, multigrid exhibits extremely rapid convergence, and actually solves the problem in the minimal possible time. The original algorithm uses rediscretization of the partial differential equation (POE) on each grid in the hierarchy of coarse grids that are used. However, this approach would not work for more complicated problems, such as problems on complicated domains and nonuniform grids, problems with variable coefficients, and non symmetric and indefinite equations. In these cases, matrix-based multi grid methods are in order.

关键词： Computational Mathematics and numerical Analysis Numeric Computing Mathematics of Computing Applications of Mathematics

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