Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations PDF Download

Author: Tarek Mathew
Publisher: Springer Science & Business Media
ISBN: 354077209X
Category : Mathematics
Languages : en
Pages : 775

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Book Description
Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.

Author: Juergen Geiser
Publisher:
ISBN: 9781138114142
Category :
Languages : en
Pages : 0

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Book Description
Exploring iterative operator-splitting methods, this work describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It generalizes the numerical analysis with respect to the consistency and stability to nonlinear, stiff, and spatial decomposed splitting problems. The book focuses on parabolic and hyperbolic equations, including convection-diffusion-reaction, heat, and wave equations, and applies the results to computational science issues, such as flow problems, elastic-wave propagation, heat transfer, and micromagnetic problems. Software tools are listed in an appendix.

Author: Kansari Haldar
Publisher: CRC Press
ISBN: 1498716342
Category : Mathematics
Languages : en
Pages : 281

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Book Description
A Powerful Methodology for Solving All Types of Differential EquationsDecomposition Analysis Method in Linear and Non-Linear Differential Equations explains how the Adomian decomposition method can solve differential equations for the series solutions of fundamental problems in physics, astrophysics, chemistry, biology, medicine, and other scientif

Author: Barry Smith
Publisher: Cambridge University Press
ISBN: 9780521602860
Category : Computers
Languages : en
Pages : 244

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Book Description
Presents an easy-to-read discussion of domain decomposition algorithms, their implementation and analysis. Ideal for graduate students about to embark on a career in computational science. It will also be a valuable resource for all those interested in parallel computing and numerical computational methods.

Author: Snehashish Chakraverty
Publisher: John Wiley & Sons
ISBN: 1119423449
Category : Mathematics
Languages : en
Pages : 256

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Book Description
Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM). Other topics covered include: emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach; combined and hybrid methods for solving differential equations; as well as an overview of fractal differential equations. Further, uncertainty in term of intervals and fuzzy numbers have also been included, along with the interval finite element method. This book: Discusses various methods for solving linear and nonlinear ODEs and PDEs Covers basic numerical techniques for solving differential equations along with various discretization methods Investigates nonlinear differential equations using semi-analytical methods Examines differential equations in an uncertain environment Includes a new scenario in which uncertainty (in term of intervals and fuzzy numbers) has been included in differential equations Contains solved example problems, as well as some unsolved problems for self-validation of the topics covered Advanced Numerical and Semi Analytical Methods for Differential Equations is an excellent text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically.

Author: G. Adomian
Publisher: Springer Science & Business Media
ISBN: 9401582890
Category : Science
Languages : en
Pages : 367

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Book Description
The Adomian decomposition method enables the accurate and efficient analytic solution of nonlinear ordinary or partial differential equations without the need to resort to linearization or perturbation approaches. It unifies the treatment of linear and nonlinear, ordinary or partial differential equations, or systems of such equations, into a single basic method, which is applicable to both initial and boundary-value problems. This volume deals with the application of this method to many problems of physics, including some frontier problems which have previously required much more computationally-intensive approaches. The opening chapters deal with various fundamental aspects of the decomposition method. Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffing equation, boundary-value problems with closed irregular contours or surfaces, and other frontier areas. The potential application of this method to a wide range of problems in diverse disciplines such as biology, hydrology, semiconductor physics, wave propagation, etc., is highlighted. For researchers and graduate students of physics, applied mathematics and engineering, whose work involves mathematical modelling and the quantitative solution of systems of equations.

Author: Juergen Geiser
Publisher: CRC Press
ISBN: 1439869839
Category : Mathematics
Languages : en
Pages : 325

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Book Description
Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations.In th

Author: Andrea Toselli
Publisher: Springer Science & Business Media
ISBN: 3540266623
Category : Mathematics
Languages : en
Pages : 454

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Book Description
This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.

Author: Olaf Steinbach
Publisher: Springer Science & Business Media
ISBN: 9783540002772
Category : Computers
Languages : en
Pages : 132

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Book Description
Domain decomposition methods are a well established tool for an efficient numerical solution of partial differential equations, in particular for the coupling of different model equations and of different discretization methods. Based on the approximate solution of local boundary value problems either by finite or boundary element methods, the global problem is reduced to an operator equation on the skeleton of the domain decomposition. Different variational formulations then lead to hybrid domain decomposition methods.

Author: John E. Lagnese
Publisher: Birkhäuser
ISBN: 3034878850
Category : Mathematics
Languages : en
Pages : 454

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Book Description
While domain decomposition methods have a long history dating back well over one hundred years, it is only during the last decade that they have become a major tool in numerical analysis of partial differential equations. This monograph emphasizes domain decomposition methods in the context of so-called virtual optimal control problems and treats optimal control problems for partial differential equations and their decompositions using an all-at-once approach.