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.

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

Download or read book Numerical Methods in Geotechnical Engineering IX written by António S. Cardoso and published by CRC Press. This book was released on 2018-06-19 with total page 1656 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods in Geotechnical Engineering IX contains 204 technical and scientific papers presented at the 9th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE2018, Porto, Portugal, 25—27 June 2018). The papers cover a wide range of topics in the field of computational geotechnics, providing an overview of recent developments on scientific achievements, innovations and engineering applications related to or employing numerical methods. They deal with subjects from emerging research to engineering practice, and are grouped under the following themes: Constitutive modelling and numerical implementation Finite element, discrete element and other numerical methods. Coupling of diverse methods Reliability and probability analysis Large deformation – large strain analysis Artificial intelligence and neural networks Ground flow, thermal and coupled analysis Earthquake engineering, soil dynamics and soil-structure interactions Rock mechanics Application of numerical methods in the context of the Eurocodes Shallow and deep foundations Slopes and cuts Supported excavations and retaining walls Embankments and dams Tunnels and caverns (and pipelines) Ground improvement and reinforcement Offshore geotechnical engineering Propagation of vibrations Following the objectives of previous eight thematic conferences, (1986 Stuttgart, Germany; 1990 Santander, Spain; 1994 Manchester, United Kingdom; 1998 Udine, Italy; 2002 Paris, France; 2006 Graz, Austria; 2010 Trondheim, Norway; 2014 Delft, The Netherlands), Numerical Methods in Geotechnical Engineering IX updates the state-of-the-art regarding the application of numerical methods in geotechnics, both in a scientific perspective and in what concerns its application for solving practical boundary value problems. The book will be much of interest to engineers, academics and professionals involved or interested in Geotechnical Engineering.

Download or read book Absorbing Boundaries and Layers Domain Decomposition Methods written by L. Tourrette and published by Nova Publishers. This book was released on 2001 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: CD-ROM contains: Sections omitted from printing of text.

Download or read book Numerical Methods in Geotechnical Engineering IX Volume 1 written by Manuel de Matos Fernandes and published by CRC Press. This book was released on 2018-06-22 with total page 935 pages. Available in PDF, EPUB and Kindle. Book excerpt: NUMGE 2018 is the ninth in a series of conferences on Numerical Methods in Geotechnical Engineering organized by the ERTC7 under the auspices of the International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE). The first conference was held in 1986 in Stuttgart, Germany and the series continued every four years (1990 Santander, Spain; 1994 Manchester, United Kingdom; 1998 Udine, Italy; 2002 Paris, France; 2006 Graz, Austria; 2010 Trondheim, Norway; 2014 Delft, The Netherlands). The conference provides a forum for exchange of ideas and discussion on topics related to numerical modelling in geotechnical engineering. Both senior and young researchers, as well as scientists and engineers from Europe and overseas, are invited to attend this conference to share and exchange their knowledge and experiences. This work is the first volume of NUMGE 2018.

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.

Download or read book Numerical Methods for Wave Equations in Geophysical Fluid Dynamics written by Dale R. Durran and published by Springer Science & Business Media. This book was released on 1998-11-25 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering a wide range of techniques, this book describes methods for the solution of partial differential equations which govern wave propagation and are used in modeling atmospheric and oceanic flows. The presentation establishes a concrete link between theory and practice.

Download or read book Combined Methods for Elliptic Equations with Singularities Interfaces and Infinities written by Zi Cai Li and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author sets out to answer two important questions: 1. Which numerical methods may be combined together? 2. How can different numerical methods be matched together? In doing so the author presents a number of useful combinations, for instance, the combination of various FEMs, the combinations of FEM-FDM, REM-FEM, RGM-FDM, etc. The combined methods have many advantages over single methods: high accuracy of solutions, less CPU time, less computer storage, easy coupling with singularities as well as the complicated boundary conditions. Since coupling techniques are essential to combinations, various matching strategies among different methods are carefully discussed. The author provides the matching rules so that optimal convergence, even superconvergence, and optimal stability can be achieved, and also warns of the matching pitfalls to avoid. Audience: The book is intended for both mathematicians and engineers and may be used as text for advanced students.

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.

Download or read book Numerical Methods For Elliptic Problems With Singularities Boundary Mtds And Nonconforming Combinatn written by Zi-cai Li and published by World Scientific. This book was released on 1990-12-27 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Download or read book Domain Decomposition Methods in Science and Engineering XVI written by Olof B. Widlund and published by Springer Science & Business Media. This book was released on 2007-01-19 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition is an active research area concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models of natural and engineered systems. The present volume sets forth new contributions in areas of numerical analysis, computer science, scientific and industrial applications, and software development.

Download or read book The Finite Element Method Set written by Olek C Zienkiewicz and published by Elsevier. This book was released on 2005-11-25 with total page 1872 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sixth editions of these seminal books deliver the most up to date and comprehensive reference yet on the finite element method for all engineers and mathematicians. Renowned for their scope, range and authority, the new editions have been significantly developed in terms of both contents and scope. Each book is now complete in its own right and provides self-contained reference; used together they provide a formidable resource covering the theory and the application of the universally used FEM. Written by the leading professors in their fields, the three books cover the basis of the method, its application to solid mechanics and to fluid dynamics. * This is THE classic finite element method set, by two the subject's leading authors * FEM is a constantly developing subject, and any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in these books * Fully up-to-date; ideal for teaching and reference

Download or read book Time Domain Scattering written by P. A. Martin and published by Cambridge University Press. This book was released on 2021-06-24 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The wave equation, a classical partial differential equation, has been studied and applied since the eighteenth century. Solving it in the presence of an obstacle, the scatterer, can be achieved using a variety of techniques and has a multitude of applications. This book explains clearly the fundamental ideas of time-domain scattering, including in-depth discussions of separation of variables and integral equations. The author covers both theoretical and computational aspects, and describes applications coming from acoustics (sound waves), elastodynamics (waves in solids), electromagnetics (Maxwell's equations) and hydrodynamics (water waves). The detailed bibliography of papers and books from the last 100 years cement the position of this work as an essential reference on the topic for applied mathematicians, physicists and engineers.

Download or read book Computational Acoustics of Noise Propagation in Fluids Finite and Boundary Element Methods written by Steffen Marburg and published by Springer Science & Business Media. This book was released on 2008-02-27 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a survey of numerical methods for acoustics, namely the finite element method (FEM) and the boundary element method (BEM). It is the first book summarizing FEM and BEM (and optimization) for acoustics. The book shows that both methods can be effectively used for many other cases, FEM even for open domains and BEM for closed ones. Emphasis of the book is put on numerical aspects and on treatment of the exterior problem in acoustics, i.e. noise radiation.

Download or read book An Introduction to Domain Decomposition Methods written by Victorita Dolean and published by SIAM. This book was released on 2015-12-08 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to offer an overview of the most popular domain decomposition methods for partial differential equations (PDEs). These methods are widely used for numerical simulations in solid mechanics, electromagnetism, flow in porous media, etc., on parallel machines from tens to hundreds of thousands of cores. The appealing feature of domain decomposition methods is that, contrary to direct methods, they are naturally parallel. The authors focus on parallel linear solvers. The authors present all popular algorithms, both at the PDE level and at the discrete level in terms of matrices, along with systematic scripts for sequential implementation in a free open-source finite element package as well as some parallel scripts. Also included is a new coarse space construction (two-level method) that adapts to highly heterogeneous problems.

Download or read book Numerical and Analytical Methods for Scientists and Engineers Using Mathematica written by Daniel Dubin and published by Wiley-Interscience. This book was released on 2003-05-05 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.