Download or read book Numerical Methods For Exterior Problems written by Lung-an Ying and published by World Scientific. This book was released on 2006-11-21 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Discrete Numerical Methods in Physics and Engineering written by Greenspan and published by Academic Press. This book was released on 1974-05-31 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete Numerical Methods in Physics and Engineering
Download or read book Fitted Numerical Methods For Singular Perturbation Problems Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions Revised Edition written by John J H Miller and published by World Scientific. This book was released on 2012-02-29 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.
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 Elliptic Problems with Singularities written by Zi-Cai Li and published by World Scientific. This book was released on 1990 with total page 286 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 Exterior Calculus written by Douglas N. Arnold and published by SIAM. This book was released on 2018-12-12 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world?wave propagation, thermodynamics, fluid flow, solid deformation, electricity and magnetism, quantum mechanics, general relativity, and many more?are described by differential equations. We depend on numerical methods for the ability to simulate, explore, predict, and control systems involving these processes. The finite element exterior calculus, or FEEC, is a powerful new theoretical approach to the design and understanding of numerical methods to solve partial differential equations (PDEs). The methods derived with FEEC preserve crucial geometric and topological structures underlying the equations and are among the most successful examples of structure-preserving methods in numerical PDEs. This volume aims to help numerical analysts master the fundamentals of FEEC, including the geometrical and functional analysis preliminaries, quickly and in one place. It is also accessible to mathematicians and students of mathematics from areas other than numerical analysis who are interested in understanding how techniques from geometry and topology play a role in numerical PDEs.
Download or read book Fitted Numerical Methods For Singular Perturbation Problems Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions written by John J H Miller and published by World Scientific. This book was released on 1996-01-01 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first edition of this book the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In this revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.
Download or read book Numerical Analysis and Its Applications written by Ivan Dimov and published by Springer. This book was released on 2017-04-11 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes thoroughly revised selected papers of the 6th International Conference on Numerical Analysis and Its Applications, NAA 2016, held in Lozenetz, Bulgaria, in June 2016. The 90 revised papers presented were carefully reviewed and selected from 98 submissions. The conference offers a wide range of the following topics: Numerical Modeling; Numerical Stochastics; Numerical Approx-imation and Computational Geometry; Numerical Linear Algebra and Numer-ical Solution of Transcendental Equations; Numerical Methods for Differential Equations; High Performance Scientific Computing; and also special topics such as Novel methods in computational finance based on the FP7 Marie Curie Action,Project Multi-ITN STRIKE - Novel Methods in Compu-tational Finance, Grant Agreement Number 304617; Advanced numerical and applied studies of fractional differential equations.
Download or read book Numerical Methods written by V. Pereyra and published by Springer. This book was released on 2007-12-03 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: a
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.
Download or read book Topics in Boundary Element Research written by Carlos A. Brebbia and published by Springer. This book was released on 2013-12-19 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series has been developed in response to the interest shown in boundary ele ments by scientists and engineers. Whilst Volume I was dedicated to basic principles and applications, this book is concerned with the state of the art in the solution of time-dependent problems. Since papers have recently been published on this im portant topic it is time to produce a work ofa morepermanent nature. The volume begins with a chapter on the Fundamentals of Boundary Integral Equation Methods in Elastodynamics. After reviewing the basic equations of elasto dynamics, the wave equation and dynamic reciprocal theorems are stated and the direct and indirect boundary element formulations are presented. Eigenvalue problems are discussed together with the case of the Fourier transformations. Several applications illustrate the etfectiveness ofthe technique for engineering. Chapter 2 examines some ofthe various boundary integral equation formulations available for elastodynamic problems. In particular the displacement-traction for mulation is compared with the displacement-potential case. The special character istics ofthe elastodynamics fundamental solutions are discussed in detail and a criti cal comparison with the elastostatics case is presented. While the chapter is not meant to be a complete review of the work in the field, the original presentation of the problern and the suggestions for further work make an important contribu tion to the development ofthe method.
Download or read book A Theoretical Introduction to Numerical Analysis written by Victor S. Ryaben'kii and published by CRC Press. This book was released on 2006-11-02 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study. An access
Download or read book Mathematical Analysis and Numerical Methods for Science and Technology written by Robert Dautray and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: The advent of high-speed computers has made it possible for the first time to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical and industrial activity has been affected by these developments. The objective of the present work is to compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form.
Download or read book A Numerical Method for the Exterior Dirichlet Problem for the Reduced Wave Equation written by Donald Greenspan and published by . This book was released on 1966 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: A digital computer technique for approximating the solution of the exterior Dirichlet problem for the reduced wave equation is described and discussed. (Author).
Download or read book Numerical Methods for Initial Value Problems in Ordinary Differential Equations written by Simeon Ola Fatunla and published by Academic Press. This book was released on 2014-05-10 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Method for Initial Value Problems in Ordinary Differential Equations deals with numerical treatment of special differential equations: stiff, stiff oscillatory, singular, and discontinuous initial value problems, characterized by large Lipschitz constants. The book reviews the difference operators, the theory of interpolation, first integral mean value theorem, and numerical integration algorithms. The text explains the theory of one-step methods, the Euler scheme, the inverse Euler scheme, and also Richardson's extrapolation. The book discusses the general theory of Runge-Kutta processes, including the error estimation, and stepsize selection of the R-K process. The text evaluates the different linear multistep methods such as the explicit linear multistep methods (Adams-Bashforth, 1883), the implicit linear multistep methods (Adams-Moulton scheme, 1926), and the general theory of linear multistep methods. The book also reviews the existing stiff codes based on the implicit/semi-implicit, singly/diagonally implicit Runge-Kutta schemes, the backward differentiation formulas, the second derivative formulas, as well as the related extrapolation processes. The text is intended for undergraduates in mathematics, computer science, or engineering courses, andfor postgraduate students or researchers in related disciplines.
Download or read book Numerical Methods for Eulerian and Lagrangian Conservation Laws written by Bruno Després and published by Birkhäuser. This book was released on 2017-07-09 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what is specific to and beneficial in the Lagrangian approach and its numerical methods. The two first chapters present a selection of well-known features of conservation laws and prepare readers for the subsequent chapters, which are dedicated to the analysis and discretization of Lagrangian systems. The text is at the frontier of applied mathematics and scientific computing and appeals to students and researchers interested in Lagrangian-based computational fluid dynamics. It also serves as an introduction to the recent corner-based Lagrangian finite volume techniques.
