Seventh Copper Mountain Conference on Multigrid Methods PDF Download
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Author: N. Duane Melson
Publisher:
ISBN:
Category :
Languages : en
Pages : 440
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Author: N. Duane Melson
Publisher:
ISBN:
Category :
Languages : en
Pages : 440
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Author: Jan Mandel
Publisher: SIAM
ISBN: 9780898712483
Category : Mathematics
Languages : en
Pages : 462
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Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 372
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Author: Yair Shapira
Publisher: Springer Science & Business Media
ISBN: 1475737262
Category : Mathematics
Languages : en
Pages : 225
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Book Description
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.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 364
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Category : Differential equations, Partial
Languages : en
Pages :
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Author:
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ISBN:
Category : Differential equations, Partial
Languages : en
Pages :
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Author: Stephen F. McCormick
Publisher: SIAM
ISBN: 1611971055
Category : Mathematics
Languages : en
Pages : 292
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Book Description
A thoughtful consideration of the current level of development of multigrid methods, this volume is a carefully edited collection of papers that addresses its topic on several levels. The first three chapters orient the reader who is familiar with standard numerical techniques to multigrid methods, first by discussing multigrid in the context of standard techniques, second by detailing the mechanics of use of the method, and third by applying the basic method to some current problems in fluid dynamics. The fourth chapter provides a unified development, complete with theory, of algebraic multigrid (AMG), which is a linear equation solver based on multigrid principles. The last chapter is an ambitious development of a very general theory of multigrid methods for variationally posed problems. Included as an appendix is the latest edition of the Multigrid Bibliography, an attempted compilation of all existing research publications on multigrid.
Author: Erik Dick
Publisher: Springer Science & Business Media
ISBN: 3642583121
Category : Mathematics
Languages : en
Pages : 306
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Book Description
This volume contains 39 of the papers presented at the Sixth European Multigrid Conference, held in Gent, Belgium, September 27-30, 1999. The topics treated at the conference cover all aspects of Multigrid Methods: theory, analysis, computer implementation, applications in the fields of physics, chemistry, fluid mechanics, structural mechanics and magnetism.
Author: Robert L May
Publisher: World Scientific
ISBN: 981454728X
Category :
Languages : en
Pages : 902
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Book Description
This proceedings contains seven invited papers and 100 contributed papers. The topics covered range from studies of theoretical aspects of computational methods through to simulations of large-scale industrial processes, with an emphasis on the efficient use of computers to solve practical problems. Developers and users of computational techniques who wish to keep up with recent developments in the application of modern computational technology to problems in science and engineering will find much of interest in this volume.
