The Numerical Solution Of Elliptic Equations

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The Numerical Solution Of Elliptic Equations

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Author : Garrett Birkhoff
language : en
Publisher: SIAM
Release Date : 1971-01-01

The Numerical Solution Of Elliptic Equations written by Garrett Birkhoff and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-01-01 with Mathematics categories.

A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing?the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore realistic models of problems arising in the natural sciences and engineering.

Numerical Solution Of Elliptic And Parabolic Partial Differential Equations With Cd Rom

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Author : John Arthur Trangenstein
language : en
Publisher: Cambridge University Press
Release Date : 2013-04-18

Numerical Solution Of Elliptic And Parabolic Partial Differential Equations With Cd Rom written by John Arthur Trangenstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.

For mathematicians and engineers interested in applying numerical methods to physical problems this book is ideal. Numerical ideas are connected to accompanying software, which is also available online. By seeing the complete description of the methods in both theory and implementation, students will more easily gain the knowledge needed to write their own application programs or develop new theory. The book contains careful development of the mathematical tools needed for analysis of the numerical methods, including elliptic regularity theory and approximation theory. Variational crimes, due to quadrature, coordinate mappings, domain approximation and boundary conditions, are analyzed. The claims are stated with full statement of the assumptions and conclusions, and use subscripted constants which can be traced back to the origination (particularly in the electronic version, which can be found on the accompanying CD-ROM).

Numerical Solution Of Elliptic Differential Equations By Reduction To The Interface

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Author : Boris N. Khoromskij
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Numerical Solution Of Elliptic Differential Equations By Reduction To The Interface written by Boris N. Khoromskij 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.

During the last decade essential progress has been achieved in the analysis and implementation of multilevel/rnultigrid and domain decomposition methods to explore a variety of real world applications. An important trend in mod ern numerical simulations is the quick improvement of computer technology that leads to the well known paradigm (see, e. g. , [78,179]): high-performance computers make it indispensable to use numerical methods of almost linear complexity in the problem size N, to maintain an adequate scaling between the computing time and improved computer facilities as N increases. In the h-version of the finite element method (FEM), the multigrid iteration real izes an O(N) solver for elliptic differential equations in a domain n c IRd d with N = O(h- ) , where h is the mesh parameter. In the boundary ele ment method (BEM) , the traditional panel clustering, fast multi-pole and wavelet based methods as well as the modern hierarchical matrix techniques are known to provide the data-sparse approximations to the arising fully populated stiffness matrices with almost linear cost O(Nr log?Nr), where 1 d Nr = O(h - ) is the number of degrees of freedom associated with the boundary. The aim of this book is to introduce a wider audience to the use of a new class of efficient numerical methods of almost linear complexity for solving elliptic partial differential equations (PDEs) based on their reduction to the interface.

The Numerical Solution Of Elliptic Equations

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Author :
language : en
Publisher:
Release Date : 1971

The Numerical Solution Of Elliptic 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 1971 with categories.

Numerical Methods For Partial Differential Equations

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Author : William F. Ames
language : en
Publisher:
Release Date : 1970

Numerical Methods For Partial Differential Equations written by William F. Ames and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.

Elliptic Differential Equations

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Author : Wolfgang Hackbusch
language : en
Publisher: Springer
Release Date : 2017-06-01

Elliptic Differential Equations written by Wolfgang Hackbusch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-01 with Mathematics categories.

This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.

Numerical Solution Of Elliptic And Parabolic Partial Differential Equations

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Author : John Arthur Trangenstein
language : en
Publisher:
Release Date : 2013

Numerical Solution Of Elliptic And Parabolic Partial Differential Equations written by John Arthur Trangenstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with MATHEMATICS categories.

For mathematicians and engineers interested in applying numerical methods to physical problems this book is ideal. Numerical ideas are connected to accompanying software, which is also available online. By seeing the complete description of the methods in both theory and implementation, students will more easily gain the knowledge needed to write their own application programs or develop new theory. The book contains careful development of the mathematical tools needed for analysis of the numerical methods, including elliptic regularity theory and approximation theory. Variational crimes, due to quadrature, coordinate mappings, domain approximation and boundary conditions, are analyzed. The claims are stated with full statement of the assumptions and conclusions, and use subscripted constants which can be traced back to the origination (particularly in the electronic version, which can be found on the accompanying CD-ROM).

Numerical Methods For Elliptic Problems With Singularities

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Author : Zi-Cai Li
language : en
Publisher: World Scientific
Release Date : 1990

Numerical Methods For Elliptic Problems With Singularities written by Zi-Cai Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.

This book presents two kinds of numerical methods for solving elliptic boundary value problems with singularities. Part I gives the boundary methods which use analytic and singular expansions, and Part II the nonconforming methods combining finite element methods (FEM) (or finite difference methods (FDM)) and singular (or analytic) expansions. The advantage of these methods over the standard FEM and FDM is that they can cope with complicated geometrical boundaries and boundary conditions as well as singularity. Therefore, accurate numerical solutions near singularities can be obtained. The description of methods, error bounds, stability analysis and numerical experiments are provided for the typical problems with angular, interface and infinity singularities. However, the approximate techniques and coupling strategy given can be applied to solving other PDE and engineering problems with singularities as well. This book is derived from the author's Ph. D. thesis which won the 1987 best doctoral dissertation award given by the Canadian Applied Mathematics Society.

Algorithms For Elliptic Problems

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Author : Marián Vajtersic
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Algorithms For Elliptic Problems written by Marián Vajtersic 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 2013-03-09 with Computers categories.

This volume deals with problems of modern effective algorithms for the numerical solution of the most frequently occurring elliptic partial differential equations. From the point of view of implementation, attention is paid to algorithms for both classical sequential and parallel computer systems. The first two chapters are devoted to fast algorithms for solving the Poisson and biharmonic equation. In the third chapter, parallel algorithms for model parallel computer systems of the SIMD and MIMD types are described. The implementation aspects of parallel algorithms for solving model elliptic boundary value problems are outlined for systems with matrix, pipeline and multiprocessor parallel computer architectures. A modern and popular multigrid computational principle which offers a good opportunity for a parallel realization is described in the next chapter. More parallel variants based in this idea are presented, whereby methods and assignments strategies for hypercube systems are treated in more detail. The last chapter presents VLSI designs for solving special tridiagonal linear systems of equations arising from finite-difference approximations of elliptic problems. For researchers interested in the development and application of fast algorithms for solving elliptic partial differential equations using advanced computer systems.

Numerical Methods For Elliptic Problems With Singularities Boundary Mtds And Nonconforming Combinatn

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Author : Zi-cai Li
language : en
Publisher: World Scientific
Release Date : 1990-12-27

Numerical Methods For Elliptic Problems With Singularities Boundary Mtds And Nonconforming Combinatn written by Zi-cai Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-12-27 with Mathematics categories.

This book presents two kinds of numerical methods for solving elliptic boundary value problems with singularities. Part I gives the boundary methods which use analytic and singular expansions, and Part II the nonconforming methods combining finite element methods (FEM) (or finite difference methods (FDM)) and singular (or analytic) expansions. The advantage of these methods over the standard FEM and FDM is that they can cope with complicated geometrical boundaries and boundary conditions as well as singularity. Therefore, accurate numerical solutions near singularities can be obtained. The description of methods, error bounds, stability analysis and numerical experiments are provided for the typical problems with angular, interface and infinity singularities. However, the approximate techniques and coupling strategy given can be applied to solving other PDE and engineering problems with singularities as well. This book is derived from the author's Ph. D. thesis which won the 1987 best doctoral dissertation award given by the Canadian Applied Mathematics Society.