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Numerical Methods for Problems in Infinite Domains

Numerical Methods for Problems in Infinite Domains Author D. Givoli
ISBN-10 9781483291086
Release 2013-10-22
Pages 316
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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

Numerical Methods for Exterior Problems Author Long'an Ying
ISBN-10 9789812772565
Release 2006
Pages 269
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This book provides a comprehensive introduction to the numerical methods for the exterior problems in partial differential equations frequently encountered in science and engineering computing. The coverage includes both traditional and novel methods. A concise introduction to the well-posedness of the problems is given, establishing a solid foundation for the methods. Sample Chapter(s). Chapter 1: Exterior Problems of Partial Differential Equations (1,839 KB). Contents: Exterior Problems of Partial Differential Equations; Boundary Element Method; Infinite Element Method; Artificial Boundary Conditions; Perfectly Matched Layer Method; Spectral Method. Readership: Researchers in numerical and computational mathematics; also useful as a textbook for graduate students.



Numerical Analysis of Partial Differential Equations

Numerical Analysis of Partial Differential Equations Author S. H, Lui
ISBN-10 9781118111116
Release 2012-01-10
Pages 480
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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.



Absorbing Boundaries and Layers Domain Decomposition Methods

Absorbing Boundaries and Layers  Domain Decomposition Methods Author L. Tourrette
ISBN-10 1560729406
Release 2001
Pages 380
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CD-ROM contains: Sections omitted from printing of text.



Numerical Methods in Geotechnical Engineering IX Volume 1

Numerical Methods in Geotechnical Engineering IX  Volume 1 Author Manuel de Matos Fernandes
ISBN-10 9780429823190
Release 2018-06-22
Pages 900
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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.



Dynamic and Transient Infinite Elements

Dynamic and Transient Infinite Elements Author Chongbin Zhao
ISBN-10 3642008461
Release 2009-06-23
Pages 259
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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 Based on Sinc and Analytic Functions

Numerical Methods Based on Sinc and Analytic Functions Author Frank Stenger
ISBN-10 9781461227069
Release 2012-12-06
Pages 565
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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.



Numerical Methods for Elliptic Problems with Singularities

Numerical Methods for Elliptic Problems with Singularities Author Zi-Cai Li
ISBN-10 981020292X
Release 1990
Pages 258
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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.



Numerical Methods for Elliptic Problems with Singularities

Numerical Methods for Elliptic Problems with Singularities Author Zi-Cai Li
ISBN-10 981020292X
Release 1990
Pages 258
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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.



Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations

Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations Author Sergej S. Artemiev
ISBN-10 9067642509
Release 1997
Pages 176
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This book deals with numerical analysis of systems of both ordinary and stochastic differential equations. The first chapter is devoted to numerical solution problems of the Cauchy problem for stiff ordinary differential equation (ODE) systems by Rosenbrock-type methods (RTMs). Here, general solutions of consistency equations are obtained, which lead to the construction of RTMs from the first to the fourth order. The second chapter deals with statistical simulation problems of the solution of the Cauchy problem for stochastic differential equation (SDE) systems. The mean-square convergence theorem is considered, as well as Taylor expansions of numerical solutions. Also included are applications of numerical methods of SDE solutions to partial differential equations and to analysis and synthesis problems of automated control of stochastic systems.



Wave Propagation in Infinite Domains

Wave Propagation in Infinite Domains Author Lutz Lehmann
ISBN-10 9783540711094
Release 2007-05-24
Pages 185
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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.



Instabilities of Flows With and Without Heat Transfer and Chemical Reaction

Instabilities of Flows  With and Without Heat Transfer and Chemical Reaction Author Tapan Sengupta
ISBN-10 9783709101278
Release 2010-04-03
Pages 330
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The articles in the book treat flow instability and transition starting with classical material dealt with in an innovative and rigorous way, some newer physical mechanisms explained for the first time and finally with the very complex topic of bombustion and two-phase flow instabilities.



Time Dependent Problems and Difference Methods

Time Dependent Problems and Difference Methods Author Bertil Gustafsson
ISBN-10 9781118548523
Release 2013-07-18
Pages 528
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Praise for the First Edition ". . . fills a considerable gap in the numerical analysis literature by providing a self-contained treatment . . . this is an important work written in a clear style . . . warmly recommended to any graduate student or researcher in the field of the numerical solution of partial differential equations." —SIAM Review Time-Dependent Problems and Difference Methods, Second Edition continues to provide guidance for the analysis of difference methods for computing approximate solutions to partial differential equations for time-dependent problems. The book treats differential equations and difference methods with a parallel development, thus achieving a more useful analysis of numerical methods. The Second Edition presents hyperbolic equations in great detail as well as new coverage on second-order systems of wave equations including acoustic waves, elastic waves, and Einstein equations. Compared to first-order hyperbolic systems, initial-boundary value problems for such systems contain new properties that must be taken into account when analyzing stability. Featuring the latest material in partial differential equations with new theorems, examples, and illustrations,Time-Dependent Problems and Difference Methods, Second Edition also includes: High order methods on staggered grids Extended treatment of Summation By Parts operators and their application to second-order derivatives Simplified presentation of certain parts and proofs Time-Dependent Problems and Difference Methods, Second Edition is an ideal reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs and to predict and investigate physical phenomena. The book is also excellent for graduate-level courses in applied mathematics and scientific computations.



A Celebration of Mathematical Modeling

A Celebration of Mathematical Modeling Author Dan Givoli
ISBN-10 1402018428
Release 2004-04-30
Pages 241
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ThisvolumecelebratestheeightiethbirthdayofJosephB. Keller. The authors who contributed to this volume belong to what can be called the Keller school of applied mathematics. They are former students, postdoctoral fellows and visiting scientists who have collaborated with Joe (some of them still do) during his long career. They all look at Joe as their ultimate (role) model. JoeKeller sdistinguishedcareerhasbeendividedbetweentheCourant Institute of Mathematical Sciences at New York University, where he received all his degrees (his PhD adviser being the great R. Courant himself) and served as a professor for 30 years, and Stanford University, where he has been since 1978. The appended photos highlight some scenes from the old days. Those who know Joe Keller s work have been always amazed by its diversity and breadth. It is considered a well-known truth that there is not a single important area in applied mathematics or physics which Keller did not contribute to. This can be appreciated, for example, by glancing through his list of publication included in this volume. App- priately, the papers in this book, written with Joe s inspiration, cover a variety of application areas; together they span the broad subject of mathematical modeling. The models discussed in the book describe the behavior of various systems such as those related to ?nance, waves, - croorganisms, shocks, DNA, ?ames, contact, optics, ?uids, bubbles and jets. Joe s activity includes many more areas, which unfortunately are not represented here."



Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II

Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II Author V G Maz'ia
ISBN-10 3764363983
Release
Pages
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Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II has been writing in one form or another for most of life. You can find so many inspiration from Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II book for free.



Third International Conference on Mathematical and Numerical Aspects of Wave Propagation

Third International Conference on Mathematical and Numerical Aspects of Wave Propagation Author Gary C. Cohen
ISBN-10 0898713501
Release 1995-01-01
Pages 808
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This volume contains the papers presented at the title conference. Speakers from 13 different countries were represented at the meeting. A broad range of topics in theoretical and applied wave propagation is covered.



SIAM Journal on Numerical Analysis

SIAM Journal on Numerical Analysis Author
ISBN-10 UCR:31210016063354
Release 2004-07
Pages
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SIAM Journal on Numerical Analysis has been writing in one form or another for most of life. You can find so many inspiration from SIAM Journal on Numerical Analysis also informative, and entertaining. Click DOWNLOAD or Read Online button to get full SIAM Journal on Numerical Analysis book for free.