Layer Resolving Grids And Transformations For Singular Perturbation Problems

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Layer Resolving Grids And Transformations For Singular Perturbation Problems

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Author : Vladimir D. Liseikin
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-11-05

Layer Resolving Grids And Transformations For Singular Perturbation Problems written by Vladimir D. Liseikin and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Mathematics categories.

No detailed description available for "Layer Resolving Grids and Transformations for Singular Perturbation Problems".

Difference Methods For Singular Perturbation Problems

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Author : Grigory I. Shishkin
language : en
Publisher: CRC Press
Release Date : 2008-09-22

Difference Methods For Singular Perturbation Problems written by Grigory I. Shishkin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-22 with Mathematics categories.

Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the ε-uniform convergence of these schemes and surveys the latest approaches important for further progress in numerical methods. The first part of the book e

Grid Generation Methods

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Author : Vladimir D. Liseikin
language : en
Publisher: Springer
Release Date : 2017-06-12

Grid Generation Methods written by Vladimir D. Liseikin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-12 with Science categories.

This text is an introduction to methods of grid generation technology in scientific computing. Special attention is given to methods developed by the author for the treatment of singularly-perturbed equations, e.g. in modeling high Reynolds number flows. Functionals of conformality, orthogonality, energy and alignment are discussed.

Numerical Geometry Grid Generation And Scientific Computing

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Author : Vladimir A. Garanzha
language : en
Publisher: Springer Nature
Release Date : 2021-09-25

Numerical Geometry Grid Generation And Scientific Computing written by Vladimir A. Garanzha and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-25 with Mathematics categories.

The focus of these conference proceedings is on research, development, and applications in the fields of numerical geometry, scientific computing and numerical simulation, particularly in mesh generation and related problems. In addition, this year’s special focus is on Delaunay triangulations and their applications, celebrating the 130th birthday of Boris Delaunay. In terms of content, the book strikes a balance between engineering algorithms and mathematical foundations. It presents an overview of recent advances in numerical geometry, grid generation and adaptation in terms of mathematical foundations, algorithm and software development and applications. The specific topics covered include: quasi-conformal and quasi-isometric mappings, hyperelastic deformations, multidimensional generalisations of the equidistribution principle, discrete differential geometry, spatial and metric encodings, Voronoi-Delaunay theory for tilings and partitions, duality in mathematical programming and numerical geometry, mesh-based optimisation and optimal control methods. Further aspects examined include iterative solvers for variational problems and algorithm and software development. The applications of the methods discussed are multidisciplinary and include problems from mathematics, physics, biology, chemistry, material science, and engineering.

Mesh Methods For Boundary Value Problems And Applications

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Author : Ildar B. Badriev
language : en
Publisher: Springer Nature
Release Date : 2022-09-14

Mesh Methods For Boundary Value Problems And Applications written by Ildar B. Badriev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-14 with Mathematics categories.

This book gathers papers presented at the 13th International Conference on Mesh Methods for Boundary-Value Problems and Applications, which was held in Kazan, Russia, in October 2020. The papers address the following topics: the theory of mesh methods for boundary-value problems in mathematical physics; non-linear mathematical models in mechanics and physics; algorithms for solving variational inequalities; computing science; and educational systems. Given its scope, the book is chiefly intended for students in the fields of mathematical modeling science and engineering. However, it will also benefit scientists and graduate students interested in these fields.

A Computational Differential Geometry Approach To Grid Generation

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Author : Vladimir D. Liseikin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

A Computational Differential Geometry Approach To Grid Generation written by Vladimir D. Liseikin 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 2013-03-14 with Science categories.

Grid technology whose achievements have significant impact on the efficiency of numerical codes still remains a rapidly advancing field of computational and applied mathematics. New achievements are being added by the creation of more sophisticated techniques, modification of the available methods, and implementation of more subtle tools as well as the results of the theories of differential equations, calculas of variations, and Riemannian geometry being applied to the formulation of grid models and analysis of grid properties. The development of comprehensive differential and variational grid gen eration techniques reviewed in the monographs of J. F. Thompson, Z. U. A. Warsi, C. W. Mastin, P. Knupp, S. Steinberg, V. D. Liseikin has been largely based on a popular concept in accordance with which a grid model realizing the required grid properties should be formulated through a linear combina tion of basic and control grid operators with weights. A typical basic grid operator is the operator responsible for the well-posedness of the grid model and construction of unfolding grids, e. g. the Laplace equations (generalized Laplace equations for surfaces) or the functional of grid smoothness which produces fixed nonfolding grids while grid clustering is controlled by source terms in differential grid formulations or by an adaptation functional in vari ational models. However, such a formulation does not obey the fundamental invariance laws with respect to parameterizations of physical geometries. It frequently results in cumbersome governing grid equations whose choice of weight and control functions provide conflicting grid requirements.

Layer Adapted Meshes For Reaction Convection Diffusion Problems

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Author : Torsten Linß
language : en
Publisher: Springer
Release Date : 2009-11-21

Layer Adapted Meshes For Reaction Convection Diffusion Problems written by Torsten Linß and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-21 with Mathematics categories.

This is a book on numerical methods for singular perturbation problems – in part- ular, stationary reaction-convection-diffusion problems exhibiting layer behaviour. More precisely, it is devoted to the construction and analysis of layer-adapted meshes underlying these numerical methods. Numerical methods for singularly perturbed differential equations have been studied since the early 1970s and the research frontier has been constantly - panding since. A comprehensive exposition of the state of the art in the analysis of numerical methods for singular perturbation problems is [141] which was p- lished in 2008. As that monograph covers a big variety of numerical methods, it only contains a rather short introduction to layer-adapted meshes, while the present book is exclusively dedicated to that subject. An early important contribution towards the optimisation of numerical methods by means of special meshes was made by N.S. Bakhvalov [18] in 1969. His paper spawned a lively discussion in the literature with a number of further meshes - ing proposed and applied to various singular perturbation problems. However, in the mid 1980s, this development stalled, but was enlivened again by G.I. Shishkin’s proposal of piecewise-equidistant meshes in the early 1990s [121,150]. Because of their very simple structure, they are often much easier to analyse than other meshes, although they give numerical approximations that are inferior to solutions on c- peting meshes. Shishkin meshes for numerous problems and numerical methods have been studied since and they are still very much in vogue.

Numerical Methods For Black Box Software In Computational Continuum Mechanics

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Author : Sergey I. Martynenko
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-10-24

Numerical Methods For Black Box Software In Computational Continuum Mechanics written by Sergey I. Martynenko and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-24 with Mathematics categories.

The organization of the material is presented as follows: This introductory chapter I represents a theoretical analysis of the computational algorithms for a numerical solution of the basic equations in continuum mechanics. In this chapter, the general requirements for computational grids, discretization, and iterative methods for black-box software are examined. Finally, a concept of a two-grid algorithm for (de-)coupled solving multidimensional non-linear (initial-)boundary value problems in continuum mechanics (multiphysics simulation) in complex domains is presented. Chapter II contains descriptions of the sequential Robust Multigrid Technique which is developed as a general-purpose solver in black-box codes. This chapter presents the main components of the Robust Multigrid Technique (RMT) used in the two-grid algorithm (Chapter I) to compute the auxiliary (structured) grid correction. This includes the generation of multigrid structures, computation of index mapping, and integral evaluation. Finite volume discretization on the multigrid structures will be explained by studying a 1D linear model problem. In addition, the algorithmic complexity of RMT and black-box optimization of the problem-dependent components of RMT are analysed. Chapter III provides a description of parallel RMT. This chapter introduces parallel RMT-based algorithms for solving the boundary value problems and initial-boundary value problems in unified manner. Section 1 presents a comparative analysis of the parallel RMT and the sequential V-cycle. Sections 2 and 3 present a geometric and an algebraic parallelism of RMT, i.e. parallelization of the smoothing iterations on the coarse and the levels. A parallel multigrid cycle will be considered in Section 4. A parallel RMT for the time-dependent problems is given in Section 5. Finally, the basic properties of parallel RMT will be summarized in Section 6. Theoretical aspects of the used algorithms for solving multidimensional problems are discussed in Chapters IV. This chapter contains the theoretical aspects of the algorithms used for the numerical solving of the resulting system of linear algebraic equations obtained from discrete multidimensional (initial-)boundary value problems.

Advances In The Applications Of Nonstandard Finite Difference Schemes

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Author : Ronald E Mickens
language : en
Publisher: World Scientific
Release Date : 2005-10-25

Advances In The Applications Of Nonstandard Finite Difference Schemes written by Ronald E Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-25 with Mathematics categories.

This volume provides a concise introduction to the methodology of nonstandard finite difference (NSFD) schemes construction and shows how they can be applied to the numerical integration of differential equations occurring in the natural, biomedical, and engineering sciences. These methods had their genesis in the work of Mickens in the 1990's and are now beginning to be widely studied and applied by other researchers. The importance of the book derives from its clear and direct explanation of NSFD in the introductory chapter along with a broad discussion of the future directions needed to advance the topic.

Advances In The Applications Of Nonstandard Finite Diffference Schemes

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Author : Ronald E. Mickens
language : en
Publisher: World Scientific
Release Date : 2005

Advances In The Applications Of Nonstandard Finite Diffference Schemes written by Ronald E. Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

This volume provides a concise introduction to the methodology of nonstandard finite difference (NSFD) schemes construction and shows how they can be applied to the numerical integration of differential equations occurring in the natural, biomedical, and engineering sciences. These methods had their genesis in the work of Mickens in the 1990's and are now beginning to be widely studied and applied by other researchers. The importance of the book derives from its clear and direct explanation of NSFD in the introductory chapter along with a broad discussion of the future directions needed to advance the topic.