Numerical Methods For Problems In Infinite Domains

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Numerical Methods for Problems in Infinite Domains

Author : D. Givoli
Publisher : Elsevier
ISBN 13 : 1483291081
Total Pages : 316 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Numerical Methods for Problems in Infinite Domains by : D. Givoli

Download or read book Numerical Methods for Problems in Infinite Domains written by D. Givoli and published by Elsevier. This book was released on 2013-10-22 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Methods for Exterior Problems

Author : Long'an Ying
Publisher : World Scientific
ISBN 13 : 9812772561
Total Pages : 282 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Numerical Methods for Exterior Problems by : Long'an Ying

Download or read book Numerical Methods for Exterior Problems written by Long'an Ying and published by World Scientific. This book was released on 2006 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface -- 1. Exterior problems of partial differential equations. 1.1. Harmonic equation-potential theory. 1.2. Poisson equations. 1.3. Poisson equations-variational formulation. 1.4. Helmholtz equations. 1.5. Linear elasticity. 1.6. Bi-harmonic equations. 1.7. Steady Navier-Stokes equations-linearized problems. 1.8. Steady Navier-Stokes equations. 1.9. Heat equation. 1.10. Wave equation. 1.11. Maxwell equations. 1.12. Darwin model -- 2. Boundary element method. 2.1. Some typical domains. 2.2. General domains. 2.3. Subdivision of the domain. 2.4. Dirichlet to Neǔmann operator. 2.5. Finite part of divergent integrals. 2.6. Numerical approximation. 2.7. Error estimates. 2.8. Domain decomposition. 2.9. Boundary perturbation -- 3. Infinite element method. 3.1. Harmonic equation-two dimensional problems. 3.2. General elements. 3.3. Harmonic equation-three dimensional problems. 3.4. Inhomogeneous equations. 3.5. Plane elasticity. 3.6. Bi-harmonic equations. 3.7. Stokes equation. 3.8. Darwin model. 3.9. Elliptic equations with variable coefficients. 3.10. Convergence -- 4. Artificial boundary conditions. 4.1. Absorbing boundary conditions. 4.2. Some approximations. 4.3. Bayliss-Turkel radiation boundary conditions. 4.4. A lower order absorbing boundary condition. 4.5. Liao extrapolation in space and time. 4.6. Maxwell equations. 4.7. Finite difference schemes. 4.8. Stationary Navier-Stokes equations -- 5. Perfectly matched layer method. 5.1. Wave equations. 5.2. Bérenger's perfectly matched layers. 5.3. Stability analysis. 5.4. Uniaxial perfectly matched layers. 5.5. Maxwell equations. 5.6. Helmholtz equations -- 6. Spectral method. 6.1. Introduction. 6.2. Orthogonal systems of polynomials. 6.3. Laguerre spectral methods. 6.4. Jacobi spectral methods. 6.5. Rational and irrational spectral methods. 6.6. Error estimates

Fundamental Numerical Methods for Electrical Engineering

Author : Stanislaw Rosloniec
Publisher : Springer Science & Business Media
ISBN 13 : 3540795197
Total Pages : 294 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Fundamental Numerical Methods for Electrical Engineering by : Stanislaw Rosloniec

Download or read book Fundamental Numerical Methods for Electrical Engineering written by Stanislaw Rosloniec and published by Springer Science & Business Media. This book was released on 2008-07-17 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stormy development of electronic computation techniques (computer systems and software), observed during the last decades, has made possible automation of data processing in many important human activity areas, such as science, technology, economics and labor organization. In a broadly understood technology area, this developmentledtoseparationofspecializedformsofusingcomputersforthedesign and manufacturing processes, that is: – computer-aided design (CAD) – computer-aided manufacture (CAM) In order to show the role of computer in the rst of the two applications m- tioned above, let us consider basic stages of the design process for a standard piece of electronic system, or equipment: – formulation of requirements concerning user properties (characteristics, para- ters) of the designed equipment, – elaboration of the initial, possibly general electric structure, – determination of mathematical model of the system on the basis of the adopted electric structure, – determination of basic responses (frequency- or time-domain) of the system, on the base of previously established mathematical model, – repeated modi cation of the adopted diagram (changing its structure or element values) in case, when it does not satisfy the adopted requirements, – preparation of design and technological documentation, – manufacturing of model (prototype) series, according to the prepared docum- tation, – testing the prototype under the aspect of its electric properties, mechanical du- bility and sensitivity to environment conditions, – modi cation of prototype documentation, if necessary, and handing over the documentation to series production. The most important stages of the process under discussion are illustrated in Fig. I. 1. xi xii Introduction Fig. I.

Finite Element Methods for Maxwell's Equations

Author : Peter Monk
Publisher : Clarendon Press
ISBN 13 : 0191545228
Total Pages : 468 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Finite Element Methods for Maxwell's Equations by : Peter Monk

Download or read book Finite Element Methods for Maxwell's Equations written by Peter Monk and published by Clarendon Press. This book was released on 2003-04-17 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Finite Difference-boundary Element Methods in Infinite and Semi-infinite Media in Geomechanics

Author : Ziad Halabi
Publisher :
ISBN 13 :
Total Pages : 496 pages
Book Rating : 4.:/5 (835 download)

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Book Synopsis Finite Difference-boundary Element Methods in Infinite and Semi-infinite Media in Geomechanics by : Ziad Halabi

Download or read book Finite Difference-boundary Element Methods in Infinite and Semi-infinite Media in Geomechanics written by Ziad Halabi and published by . This book was released on 2013 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

New Sinc Methods of Numerical Analysis

Author : Gerd Baumann
Publisher : Springer Nature
ISBN 13 : 303049716X
Total Pages : 411 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis New Sinc Methods of Numerical Analysis by : Gerd Baumann

Download or read book New Sinc Methods of Numerical Analysis written by Gerd Baumann and published by Springer Nature. This book was released on 2021-04-23 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume honors the 80th birthday of Frank Stenger who established new Sinc methods in numerical analysis.The contributions, written independently from each other, show the new developments in numerical analysis in connection with Sinc methods and approximations of solutions for differential equations, boundary value problems, integral equations, integrals, linear transforms, eigenvalue problems, polynomial approximations, computations on polyhedra, and many applications. The approximation methods are exponentially converging compared with standard methods and save resources in computation. They are applicable in many fields of science including mathematics, physics, and engineering.The ideas discussed serve as a starting point in many different directions in numerical analysis research and applications which will lead to new and unprecedented results. This book will appeal to a wide readership, from students to specialized experts.

Fluid-Solid Interaction Dynamics

Author : Jing Tang Xing
Publisher : Academic Press
ISBN 13 : 0128193530
Total Pages : 682 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Fluid-Solid Interaction Dynamics by : Jing Tang Xing

Download or read book Fluid-Solid Interaction Dynamics written by Jing Tang Xing and published by Academic Press. This book was released on 2019-08-30 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fluid-Solid Interaction Dynamics: Theory, Variational Principles, Numerical Methods and Applications gives a comprehensive accounting of fluid-solid interaction dynamics, including theory, numerical methods and their solutions for various FSI problems in engineering. The title provides the fundamental theories, methodologies and results developed in the application of FSI dynamics. Four numerical approaches that can be used with almost all integrated FSI systems in engineering are presented. Methods are linked with examples to illustrate results. In addition, numerical results are compared with available experiments or numerical data in order to demonstrate the accuracy of the approaches and their value to engineering applications. The title gives readers the state-of-the-art in theory, variational principles, numerical modeling and applications for fluid-solid interaction dynamics. Readers will be able to independently formulate models to solve their engineering FSI problems using information from this book. - Presents the state-of-the-art in fluid-solid interaction dynamics, providing theory, method and results - Takes an integrated approach to formulate, model and simulate FSI problems in engineering - Illustrates results with concrete examples - Gives four numerical approaches and related theories that are suitable for almost all integrated FSI systems - Provides the necessary information for bench scientists to independently formulate, model, and solve physical FSI problems in engineering

Computational Fluid Dynamics Review 1998 (In 2 Volumes)

Author : Mohamed M Hafez
Publisher : World Scientific
ISBN 13 : 9814495778
Total Pages : 1169 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Computational Fluid Dynamics Review 1998 (In 2 Volumes) by : Mohamed M Hafez

Download or read book Computational Fluid Dynamics Review 1998 (In 2 Volumes) written by Mohamed M Hafez and published by World Scientific. This book was released on 1998-11-20 with total page 1169 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first volume of CFD Review was published in 1995. The purpose of this new publication is to present comprehensive surveys and review articles which provide up-to-date information about recent progress in computational fluid dynamics, on a regular basis. Because of the multidisciplinary nature of CFD, it is difficult to cope with all the important developments in related areas. There are at least ten regular international conferences dealing with different aspects of CFD.It is a real challenge to keep up with all these activities and to be aware of essential and fundamental contributions in these areas. It is hoped that CFD Review will help in this regard by covering the state-of-the-art in this field.The present book contains sixty-two articles written by authors from the US, Europe, Japan and China, covering the main aspects of CFD. There are five sections: general topics, numerical methods, flow physics, interdisciplinary applications, parallel computation and flow visualization. The section on numerical methods includes grids, schemes and solvers, while that on flow physics includes incompressible and compressible flows, hypersonics and gas kinetics as well as transition and turbulence. This book should be useful to all researchers in this fast-developing field.

Artificial Boundary Method

Author : Houde Han
Publisher : Springer Science & Business Media
ISBN 13 : 3642354645
Total Pages : 434 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Artificial Boundary Method by : Houde Han

Download or read book Artificial Boundary Method written by Houde Han and published by Springer Science & Business Media. This book was released on 2013-04-13 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Artificial Boundary Method" systematically introduces the artificial boundary method for the numerical solutions of partial differential equations in unbounded domains. Detailed discussions treat different types of problems, including Laplace, Helmholtz, heat, Schrödinger, and Navier and Stokes equations. Both numerical methods and error analysis are discussed. The book is intended for researchers working in the fields of computational mathematics and mechanical engineering. Prof. Houde Han works at Tsinghua University, China; Prof. Xiaonan Wu works at Hong Kong Baptist University, China.

Dynamic and Transient Infinite Elements

Author : Chongbin Zhao
Publisher : Springer Science & Business Media
ISBN 13 : 3642008461
Total Pages : 270 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Dynamic and Transient Infinite Elements by : Chongbin Zhao

Download or read book Dynamic and Transient Infinite Elements written by Chongbin Zhao and published by Springer Science & Business Media. This book was released on 2009-06-23 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents state-of-the-art theory and the application of dynamic and transient infinite elements for simulating the far fields of infinite domains involved in many of scientific and engineering problems.

Numerical Methods in Thermal Problems

Author : Roland Wynne Lewis
Publisher :
ISBN 13 :
Total Pages : 1246 pages
Book Rating : 4.:/5 (43 download)

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Book Synopsis Numerical Methods in Thermal Problems by : Roland Wynne Lewis

Download or read book Numerical Methods in Thermal Problems written by Roland Wynne Lewis and published by . This book was released on 1983 with total page 1246 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Wave Propagation in Infinite Domains

Author : Lutz Lehmann
Publisher : Springer Science & Business Media
ISBN 13 : 3540711090
Total Pages : 185 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Wave Propagation in Infinite Domains by : Lutz Lehmann

Download or read book Wave Propagation in Infinite Domains written by Lutz Lehmann and published by Springer Science & Business Media. This book was released on 2007-05-24 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents theoretical fundamentals and applications of a new numerical model that has the ability to simulate wave propagation. Coverage examines linear waves in ideal fluids and elastic domains. In addition, the book includes a numerical simulation of wave propagation based on scalar and vector wave equations, as well as fluid-structure interaction and soil-structure interaction.

Research in Progress

Author :
Publisher :
ISBN 13 :
Total Pages : 248 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Research in Progress by :

Download or read book Research in Progress written by and published by . This book was released on 1988 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Analysis of Partial Differential Equations

Author : S. H, Lui
Publisher : John Wiley & Sons
ISBN 13 : 1118111117
Total Pages : 506 pages
Book Rating : 4.1/5 (181 download)

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Book Synopsis Numerical Analysis of Partial Differential Equations by : S. H, Lui

Download or read book Numerical Analysis of Partial Differential Equations written by S. H, Lui and published by John Wiley & Sons. This book was released on 2012-01-10 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Applied Mechanics Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 796 pages
Book Rating : 4.:/5 (26 download)

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Book Synopsis Applied Mechanics Reviews by :

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1970 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Inclusion-Based Boundary Element Method (iBEM)

Author : Huiming Yin
Publisher : Academic Press
ISBN 13 : 0128193859
Total Pages : 356 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis The Inclusion-Based Boundary Element Method (iBEM) by : Huiming Yin

Download or read book The Inclusion-Based Boundary Element Method (iBEM) written by Huiming Yin and published by Academic Press. This book was released on 2022-04-14 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Inclusion-Based Boundary Element Method (iBEM) is an innovative numerical method for the study of the multi-physical and mechanical behaviour of composite materials, linear elasticity, potential flow or Stokes fluid dynamics. It combines the basic ideas of Eshelby’s Equivalent Inclusion Method (EIM) in classic micromechanics and the Boundary Element Method (BEM) in computational mechanics. The book starts by explaining the application and extension of the EIM from elastic problems to the Stokes fluid, and potential flow problems for a multiphase material system in the infinite domain. It also shows how switching the Green’s function for infinite domain solutions to semi-infinite domain solutions allows this method to solve semi-infinite domain problems. A thorough examination of particle-particle interaction and particle-boundary interaction exposes the limitation of the classic micromechanics based on Eshelby’s solution for one particle embedded in the infinite domain, and demonstrates the necessity to consider the particle interactions and boundary effects for a composite containing a fairly high volume fraction of the dispersed materials. Starting by covering the fundamentals required to understand the method and going on to describe everything needed to apply it to a variety of practical contexts, this book is the ideal guide to this innovative numerical method for students, researchers, and engineers. The multidisciplinary approach used in this book, drawing on computational methods as well as micromechanics, helps to produce a computationally efficient solution to the multi-inclusion problem The iBEM can serve as an efficient tool to conduct virtual experiments for composite materials with various geometry and boundary or loading conditions Includes case studies with detailed examples of numerical implementation

Borehole Acoustic Logging – Theory and Methods

Author : Hua Wang
Publisher : Springer Nature
ISBN 13 : 3030514234
Total Pages : 326 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Borehole Acoustic Logging – Theory and Methods by : Hua Wang

Download or read book Borehole Acoustic Logging – Theory and Methods written by Hua Wang and published by Springer Nature. This book was released on 2020-07-30 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the principles, historical development, and applications of many acoustic logging methods, including acoustic logging-while-drilling and cased-hole logging methods. Benefiting from the rapid development of information technology, the subsurface energy resource industry is moving toward data integration to increase the efficiency of decision making through the use of advanced big data and artificial intelligence technologies, such as machine/deep learning. However, wellbore failure may happen if evaluations of risk and infrastructure are made using data mining methods without a complete understanding of the physics of borehole measurements. Processed results from borehole acoustic logging will constitute part of the input data used for data integration. Therefore, to successfully employ modern techniques for data assimilation and analysis, one must fully understand the complexity of wave mode propagation, how such propagation is influenced by the well, and the materials placed within the well (i.e., the cement, casing, and drill strings), and ultimately how waves penetrate into and are influenced by geological formations. State-of-the-art simulation methods, such as the discrete wavenumber integration method (DWM) and the finite difference method (FDM), are introduced to tackle the numerical challenges associated with models containing large material contrasts, such as the contrasts between borehole fluids and steel casings. Waveforms and pressure snapshots are shown to help the reader understand the wavefields under various conditions. Advanced data processing methods, including velocity analyses within the time and frequency domains, are utilized to extract the velocities of different modes. Furthermore, the authors discuss how various formation parameters influence the waveforms recorded in the borehole and describe the principles of both existing and potential tool designs and data acquisition schemes. This book greatly benefits from the research and knowledge generated over four decades at the Earth Resources Laboratory (ERL) of the Massachusetts Institute of Technology (MIT) under its acoustic logging program. Given its scope, the book is of interest to geophysicists (including borehole geophysicists and seismologists), petrophysicists, and petroleum engineers who are interested in formation evaluation and cementation conditions. In addition, this book is of interest to researchers in the acoustic sciences and to 4th-year undergraduate and postgraduate students in the areas of geophysics and acoustical physics.