Multilevel Projection Methods For Partial Differential Equations

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Multilevel Projection Methods For Partial Differential Equations

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Author : Stephen F. McCormick
language : en
Publisher: SIAM
Release Date : 1992-01-01

Multilevel Projection Methods For Partial Differential Equations written by Stephen F. McCormick and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.

The multilevel projection method is a new formalism that provides a framework for the development of multilevel algorithms in a very general setting. This methodology guides the choices of all the major multilevel processes, including relaxation and coarsening, and it applies directly to global or locally-refined discretizations. This book was developed from lectures at the CBMS-NSF Regional Conference on Multigrid and Multilevel Adaptive Methods for Partial Differential Equations in June 1991, and is a supplement to Multilevel Adaptive Methods for Partial Differential Equations, also written by Stephen F. McCormick.

A Parallel Multilevel Partition Of Unity Method For Elliptic Partial Differential Equations

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Author : Marc Alexander Schweitzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

A Parallel Multilevel Partition Of Unity Method For Elliptic Partial Differential Equations written by Marc Alexander Schweitzer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Multilevel Adaptive Methods For Partial Differential Equations

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Author : Stephen F. McCormick
language : en
Publisher: SIAM
Release Date : 1989-01-01

Multilevel Adaptive Methods For Partial Differential Equations written by Stephen F. McCormick and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.

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.

Asymptotic And Numerical Methods For Partial Differential Equations With Critical Parameters

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Author : H.G. Kaper
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Asymptotic And Numerical Methods For Partial Differential Equations With Critical Parameters written by H.G. Kaper and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This volume contains the proceedings of the NATO Advanced Research Workshop on "Asymptotic-induced Numerical Methods for Partial Differ ential Equations, Critical Parameters, and Domain Decomposition," held at Beaune (France), May 25-28, 1992. The purpose of the workshop was to stimulate the integration of asymp totic analysis, domain decomposition methods, and symbolic manipulation tools for the numerical solution of partial differential equations (PDEs) with critical parameters. A workshop on the same topic was held at Argonne Na tional Laboratory in February 1990. (The proceedings were published under the title Asymptotic Analysis and the Numerical Solu.tion of Partial Differ ential Equations, Hans G. Kaper and Marc Garbey, eds., Lecture Notes in Pure and Applied Mathematics. Vol. 130, ·Marcel Dekker, Inc., New York, 1991.) In a sense, the present proceedings represent a progress report on the topic area. Comparing the two sets of proceedings, we see an increase in the quantity as well as the quality of the contributions. 110re research is being done in the topic area, and the interest covers serious, nontrivial problems. We are pleased with this outcome and expect to see even more advances in the next few years as the field progresses.

Adaptive Parallel Multilevel Methods For Partial Differential Equations

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Author : Gerhard Zumbusch
language : en
Publisher:
Release Date : 2001

Adaptive Parallel Multilevel Methods For Partial Differential Equations written by Gerhard Zumbusch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.

Discrete Projection Methods For Integral Equations

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Author : Michael A. Golberg
language : en
Publisher: Computational Mechanics
Release Date : 1997

Discrete Projection Methods For Integral Equations written by Michael A. Golberg and has been published by Computational Mechanics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Engineering mathematics categories.

Discrete projection methods are analyzed for a variety of integral equations which arise from the reformulation of boundary value problems for partial differential equations. The theory is illustrated by applying it to a variety of integral equations: Fredholm, Volterra, Cauchy singular, hypersingular and boundary integral.

Fast Direct Solvers For Elliptic Pdes

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Author : Per-Gunnar Martinsson
language : en
Publisher: SIAM
Release Date : 2019-12-16

Fast Direct Solvers For Elliptic Pdes written by Per-Gunnar Martinsson and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-16 with Mathematics categories.

Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and speed in many applications. The focus is on fast algorithms for handling dense matrices that arise in the discretization of integral operators, such as the fast multipole method and fast direct solvers. While the emphasis is on techniques for dense matrices, the text also describes how similar techniques give rise to linear complexity algorithms for computing the inverse or the LU factorization of a sparse matrix resulting from the direct discretization of an elliptic PDE. This is the first textbook to detail the active field of fast direct solvers, introducing readers to modern linear algebraic techniques for accelerating computations, such as randomized algorithms, interpolative decompositions, and data-sparse hierarchical matrix representations. Written with an emphasis on mathematical intuition rather than theoretical details, it is richly illustrated and provides pseudocode for all key techniques. Fast Direct Solvers for Elliptic PDEs is appropriate for graduate students in applied mathematics and scientific computing, engineers and scientists looking for an accessible introduction to integral equation methods and fast solvers, and researchers in computational mathematics who want to quickly catch up on recent advances in randomized algorithms and techniques for working with data-sparse matrices.

Iciam 91

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Author : Robert E. O'Malley
language : en
Publisher: SIAM
Release Date : 1992-01-01

Iciam 91 written by Robert E. O'Malley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.

Proceedings -- Computer Arithmetic, Algebra, OOP.

Multiscale And Multiresolution Approaches In Turbulence Les Des And Hybrid Rans Les Methods Applications And Guidelines 2nd Edition

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Author : Pierre Sagaut
language : en
Publisher: World Scientific
Release Date : 2013-03-25

Multiscale And Multiresolution Approaches In Turbulence Les Des And Hybrid Rans Les Methods Applications And Guidelines 2nd Edition written by Pierre Sagaut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-25 with Mathematics categories.

The book aims to provide the reader with an updated general presentation of multiscale/multiresolution approaches in turbulent flow simulations. All modern approaches (LES, hybrid RANS/LES, DES, SAS) are discussed and recast in a global comprehensive framework. Both theoretical features and practical implementation details are addressed. Some full scale applications are described, to provide the reader with relevant guidelines to facilitate a future use of these methods./a

Multiscale And Multiresolution Approaches In Turbulence

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Author : Pierre Sagaut
language : en
Publisher: World Scientific
Release Date : 2013

Multiscale And Multiresolution Approaches In Turbulence written by Pierre Sagaut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Science categories.

The book aims to provide the reader with an updated general presentation of multiscale/multiresolution approaches in turbulent flow simulations. All modern approaches (LES, hybrid RANS/LES, DES, SAS) are discussed and recast in a global comprehensive framework. Both theoretical features and practical implementation details are addressed. Some full scale applications are described, to provide the reader with relevant guidelines to facilitate a future use of these methods.