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Author: D. Givoli Publisher: Elsevier ISBN: 1483291081 Category : Mathematics Languages : en Pages : 316
Book Description
This volume reviews and discusses the main numerical methods used today for solving problems in infinite domains. It also presents in detail one very effective method in this class, namely the Dirichlet-to-Neumann (DtN) finite element method. The book is intended to provide the researcher or engineer with the state-of-the-art in numerical solution methods for infinite domain problems, such as the problems encountered in acoustics and structural acoustics, fluid dynamics, meteorology, and many other fields of application. The emphasis is on the fundamentals of the various methods, and on reporting recent progress and forecasting future directions. An appendix at the end of the book provides an introduction to the essentials of the finite element method, and suggests a short list of texts on the subject which are categorized by their level of mathematics.
Author: D. Givoli Publisher: Elsevier ISBN: 1483291081 Category : Mathematics Languages : en Pages : 316
Book Description
This volume reviews and discusses the main numerical methods used today for solving problems in infinite domains. It also presents in detail one very effective method in this class, namely the Dirichlet-to-Neumann (DtN) finite element method. The book is intended to provide the researcher or engineer with the state-of-the-art in numerical solution methods for infinite domain problems, such as the problems encountered in acoustics and structural acoustics, fluid dynamics, meteorology, and many other fields of application. The emphasis is on the fundamentals of the various methods, and on reporting recent progress and forecasting future directions. An appendix at the end of the book provides an introduction to the essentials of the finite element method, and suggests a short list of texts on the subject which are categorized by their level of mathematics.
Author: S. H, Lui Publisher: John Wiley & Sons ISBN: 1118111117 Category : Mathematics Languages : en Pages : 506
Book Description
A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.
Author: Daniel Dubin Publisher: Wiley-Interscience ISBN: Category : Science Languages : en Pages : 664
Book Description
Written from the perspective of a physicist rather than a mathematician, the text focuses on modern practical applications in the physical engineering sciences, attacking these problems with a range of numerical and analytical methods, both elementary and advanced. Incorporating the widely used and highly praised Mathematica® software package, the author offers solution techniques for the partial differential equations of mathematical physics such as Poisson's equation, the wave equation, and Schrödinger's equation, including Fourier series and transforms, Green's functions, the method of characteristics, grids, Galerkin and simulation methods, elementary probability theory, and statistical methods.
Author: Peter Monk Publisher: Clarendon Press ISBN: 0191545228 Category : Mathematics Languages : en Pages : 468
Book Description
Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell's equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of numerical methods in computational electromagnetism there has also been considerable progress in the mathematical understanding of the properties of Maxwell's equations relevant to numerical analysis. The aim of this book is to provide an up to date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis is on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book. The methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book finishes with a short introduction to inverse problems in electromagnetism.
Author: Frank Stenger Publisher: Springer Science & Business Media ISBN: 1461227062 Category : Mathematics Languages : en Pages : 580
Book Description
Many mathematicians, scientists, and engineers are familiar with the Fast Fourier Transform, a method based upon the Discrete Fourier Transform. Perhaps not so many mathematicians, scientists, and engineers recognize that the Discrete Fourier Transform is one of a family of symbolic formulae called Sinc methods. Sinc methods are based upon the Sinc function, a wavelet-like function replete with identities which yield approximations to all classes of computational problems. Such problems include problems over finite, semi-infinite, or infinite domains, problems with singularities, and boundary layer problems. Written by the principle authority on the subject, this book introduces Sinc methods to the world of computation. It serves as an excellent research sourcebook as well as a textbook which uses analytic functions to derive Sinc methods for the advanced numerical analysis and applied approximation theory classrooms. Problem sections and historical notes are included.
Author: David Gottlieb Publisher: SIAM ISBN: 0898710235 Category : Technology & Engineering Languages : en Pages : 167
Book Description
A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.
Author: Dale R. Durran Publisher: Springer Science & Business Media ISBN: 1441964126 Category : Mathematics Languages : en Pages : 527
Book Description
This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of building a numerical model and the more sophisticated techniques that are now available. Finite difference methods, spectral methods, finite element method, flux-corrected methods and TVC schemes are all discussed. Throughout, the author keeps to a middle ground between the theorem-proof formalism of a mathematical text and the highly empirical approach found in some engineering publications. The book establishes a concrete link between theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. From the reviews: "...the books unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics." Physics of Atmosphere and Ocean
Author: Ziad Halabi Publisher: ISBN: Category : Languages : en Pages : 496
Book Description
The engineering problems in Geomechanics and Geotechnical fields are commonly treated through the infinite or semi-infinite media. The best approach to solve these problems numerically is by coupling a finite element or a finite difference with boundary element numerical methods. Coupling the bounded domain modelled by Flac3D, a well-known program that implements an explicit finite difference method, with the boundary element method, which satisfies exactly the governing Partial Differential Equations (PDE) in the surrounding infinite or semi-infinite medium, combines the capabilities and the advantages of both methods. The Domain Decomposition Method (DDM) partitions the task of solving the PDE into separate computations over the coupled sub-domains. This method allows the FDM (Flac3D program) and the Boundary Element Method (BEM) program to work independently and interactively. In contrast, at the level of discretized equations, the coupling method requires building a complicated unified system of equations. Therefore, a Domain Decomposition Sequential Dirichlet-Neumann Iterative Coupling Method is developed in this thesis to couple both programs. The method is applied in four cases, 2D and 3D infinite and semi-infinite domains, using the appropriate fundamental solutions in the Boundary Integral Equation required for each case. After applying this method, the mechanical responses computed by Flac3D is corrected and the same responses far from the bounded domain are computed with less computer runtime (CPU) compared with the uncoupled Flac3D solution. The method is also verified by comparing the obtained numerical results with the corresponding analytical solutions. Two BEM pre and post processing intrinsic plug-ins are created, which provide access to the data of Flac3D, as well as the internal structure of the programming language embedded within Flac3D program. These intrinsics are 10 to 100 times faster to execute than the functions created using the Flac3D embedded language. Furthermore, the complementary part of the Kernels is derived based on Mindlin's fundamental solutions. These Kernels are required to compute the stress inside the 3D semi-infinite domain.
Author: D. Givoli
Author: D. Givoli
Author: Long'an Ying
Author: S. H, Lui
Author: Daniel Dubin
Author: Peter Monk
Author: Frank Stenger
Author: David Gottlieb
Author: Carlos A. Brebbia
Author: Dale R. Durran
Author: Ziad Halabi