Optimization In Solving Elliptic Problems

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Optimization In Solving Elliptic Problems

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Author : Eugene G. D'yakonov
language : en
Publisher: CRC Press
Release Date : 2018-05-04

Optimization In Solving Elliptic Problems written by Eugene G. D'yakonov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.

Optimization in Solving Elliptic Problems focuses on one of the most interesting and challenging problems of computational mathematics - the optimization of numerical algorithms for solving elliptic problems. It presents detailed discussions of how asymptotically optimal algorithms may be applied to elliptic problems to obtain numerical solutions meeting certain specified requirements. Beginning with an outline of the fundamental principles of numerical methods, this book describes how to construct special modifications of classical finite element methods such that for the arising grid systems, asymptotically optimal iterative methods can be applied. Optimization in Solving Elliptic Problems describes the construction of computational algorithms resulting in the required accuracy of a solution and having a pre-determined computational complexity. Construction of asymptotically optimal algorithms is demonstrated for multi-dimensional elliptic boundary value problems under general conditions. In addition, algorithms are developed for eigenvalue problems and Navier-Stokes problems. The development of these algorithms is based on detailed discussions of topics that include accuracy estimates of projective and difference methods, topologically equivalent grids and triangulations, general theorems on convergence of iterative methods, mixed finite element methods for Stokes-type problems, methods of solving fourth-order problems, and methods for solving classical elasticity problems. Furthermore, the text provides methods for managing basic iterative methods such as domain decomposition and multigrid methods. These methods, clearly developed and explained in the text, may be used to develop algorithms for solving applied elliptic problems. The mathematics necessary to understand the development of such algorithms is provided in the introductory material within the text, and common specifications of algorithms that have been developed for typical problems in mathema

Efficient Solution Of Symmetric Eigenvalue Problems Using Multigrid Preconditioners In The Locally Optimal Block Conjugate Gradient Method

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Author : Andrew V. Knyazev
language : en
Publisher:
Release Date : 2001

Efficient Solution Of Symmetric Eigenvalue Problems Using Multigrid Preconditioners In The Locally Optimal Block Conjugate Gradient Method written by Andrew V. Knyazev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Conjugate gradient methods categories.

Moscow University Computational Mathematics And Cybernetics

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Author : Moskovskiĭ gosudarstvennyĭ universitet im. M.V. Lomonosova
language : en
Publisher:
Release Date : 2003

Moscow University Computational Mathematics And Cybernetics written by Moskovskiĭ gosudarstvennyĭ universitet im. M.V. Lomonosova and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Cybernetics categories.

Optimization In Elliptic Problems With Applications To Mechanics Of Deformable Bodies And Fluid Mechanics

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Author : William G. Litvinov
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Optimization In Elliptic Problems With Applications To Mechanics Of Deformable Bodies And Fluid Mechanics written by William G. Litvinov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.

This book is intended to be both a thorough introduction to contemporary research in optimization theory for elliptic systems with its numerous applications and a textbook at the undergraduate and graduate level for courses in pure or applied mathematics or in continuum mechanics. Various processes of modern technology and production are described by el liptic partial differential equations. Optimization of these processes reduces to op timization problems for elliptic systems. The numerical solution of such problems is associated with the solution of the following questions. 1. The setting of the optimization problem ensuring the existence of a solution on a set of admissible controls, which is a subset of some infinite-dimensional vector space. 2. Reduction of the infinite-dimensional optimization problem to a sequence of finite-dimensional problems such that the solutions of the finite-dimensional problems converge, in a sense, to the solution of the infinite-dimensional problem.3. Numerical solution of the finite-dimensional problems.

Hercma 2001

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Author :
language : en
Publisher:
Release Date : 2002

Hercma 2001 written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Computer science categories.

Computational Methods In Applied Mathematics

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Author :
language : en
Publisher:
Release Date : 2004

Computational Methods In Applied Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Engineering mathematics categories.

Siam Journal On Scientific Computing

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Author :
language : en
Publisher:
Release Date : 2007

Siam Journal On Scientific Computing written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematical statistics categories.

Nasa Conference Publication

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Author :
language : en
Publisher:
Release Date : 1996

Nasa Conference Publication written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Aeronautics categories.

Function Spaces Approximations And Differential Equations

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Author :
language : en
Publisher:
Release Date : 2003

Function Spaces Approximations And Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Approximation theory categories.

Optimizing Methods In Statistics

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Author : Jagdish S. Rustagi
language : en
Publisher:
Release Date : 1979

Optimizing Methods In Statistics written by Jagdish S. Rustagi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.