Computational Methods For Pde In Mechanics

Author : Berardino D'Acunto
Publisher : World Scientific Publishing Company
Page : 300 pages
File Size : 47,6 Mb
Release : 2004-10-12
Category : Electronic
ISBN : 9789813106413

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Computational Methods for PDE in Mechanics by Berardino D'Acunto Pdf

This book provides a good introduction to modern computational methods for Partial Differential Equations in Mechanics. Finite-difference methods for parabolic, hyperbolic as well as elliptic partial differential equations are discussed. A gradual and inductive approach to the numerical concepts has been used, such that the presentation of the theory is easily accessible to upper-level undergraduate and graduate students. Special attention has been given to the applications, with many examples and exercises provided along with solutions. For each type of equation, physical models are carefully derived and presented in full details. Windows programs developed in C++ language have been included in the accompanying CD-ROM. These programs can be easily modified to solve different problems, and the reader is encouraged to take full advantage of the innovative features of this powerful development tool.

Author : Hans Petter Langtangen
Publisher : Springer Science & Business Media
Page : 704 pages
File Size : 46,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662011706

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Computational Partial Differential Equations by Hans Petter Langtangen Pdf

Targeted at students and researchers in computational sciences who need to develop computer codes for solving PDEs, the exposition here is focused on numerics and software related to mathematical models in solid and fluid mechanics. The book teaches finite element methods, and basic finite difference methods from a computational point of view, with the main emphasis on developing flexible computer programs, using the numerical library Diffpack. Diffpack is explained in detail for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow. All the program examples, as well as Diffpack for use with this book, are available on the Internet. XXXXXXX NEUER TEXT This book is for researchers who need to develop computer code for solving PDEs. Numerical methods and the application of Diffpack are explained in detail. Diffpack is a modern C++ development environment that is widely used by industrial scientists and engineers working in areas such as oil exploration, groundwater modeling, and materials testing. All the program examples, as well as a test version of Diffpack, are available for free over the Internet.

Author : Stig Larsson,Vidar Thomee
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 41,6 Mb
Release : 2008-12-05
Category : Mathematics
ISBN : 9783540887058

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Partial Differential Equations with Numerical Methods by Stig Larsson,Vidar Thomee Pdf

The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

Author : Vitoriano Ruas
Publisher : John Wiley & Sons
Page : 376 pages
File Size : 46,8 Mb
Release : 2016-04-28
Category : Technology & Engineering
ISBN : 9781119111368

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Numerical Methods for Partial Differential Equations by Vitoriano Ruas Pdf

Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universités, UPMC - Université Paris 6, France A comprehensive overview of techniques for the computational solution of PDE's Numerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. The book combines clear descriptions of the three methods, their reliability, and practical implementation aspects. Justifications for why numerical methods for the main classes of PDE's work or not, or how well they work, are supplied and exemplified. Aimed primarily at students of Engineering, Mathematics, Computer Science, Physics and Chemistry among others this book offers a substantial insight into the principles numerical methods in this class of problems are based upon. The book can also be used as a reference for research work on numerical methods for PDE’s. Key features: A balanced emphasis is given to both practical considerations and a rigorous mathematical treatment The reliability analyses for the three methods are carried out in a unified framework and in a structured and visible manner, for the basic types of PDE's Special attention is given to low order methods, as practitioner's overwhelming default options for everyday use New techniques are employed to derive known results, thereby simplifying their proof Supplementary material is available from a companion website.

Author : G. Evans,J. Blackledge,P. Yardley
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447103790

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Analytic Methods for Partial Differential Equations by G. Evans,J. Blackledge,P. Yardley Pdf

This is the practical introduction to the analytical approach taken in Volume 2. Based upon courses in partial differential equations over the last two decades, the text covers the classic canonical equations, with the method of separation of variables introduced at an early stage. The characteristic method for first order equations acts as an introduction to the classification of second order quasi-linear problems by characteristics. Attention then moves to different co-ordinate systems, primarily those with cylindrical or spherical symmetry. Hence a discussion of special functions arises quite naturally, and in each case the major properties are derived. The next section deals with the use of integral transforms and extensive methods for inverting them, and concludes with links to the use of Fourier series.

Author : W. Fitzgibbon,Y.A. Kuznetsov,Pekka Neittaanmäki,Jacques Périaux,Olivier Pironneau
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 48,5 Mb
Release : 2010-01-08
Category : Science
ISBN : 9789048132393

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Applied and Numerical Partial Differential Equations by W. Fitzgibbon,Y.A. Kuznetsov,Pekka Neittaanmäki,Jacques Périaux,Olivier Pironneau Pdf

Standing at the intersection of mathematics and scientific computing, this collection of state-of-the-art papers in nonlinear PDEs examines their applications to subjects as diverse as dynamical systems, computational mechanics, and the mathematics of finance.

Author : Roland Glowinski,Pekka Neittaanmäki
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 40,8 Mb
Release : 2008-06-26
Category : Science
ISBN : 9781402087585

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Partial Differential Equations by Roland Glowinski,Pekka Neittaanmäki Pdf

For more than 250 years partial di?erential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at ?rst and then those originating from - man activity and technological development. Mechanics, physics and their engineering applications were the ?rst to bene?t from the impact of partial di?erential equations on modeling and design, but a little less than a century ago the Schr ̈ odinger equation was the key opening the door to the application of partial di?erential equations to quantum chemistry, for small atomic and molecular systems at ?rst, but then for systems of fast growing complexity. The place of partial di?erential equations in mathematics is a very particular one: initially, the partial di?erential equations modeling natural phenomena were derived by combining calculus with physical reasoning in order to - press conservation laws and principles in partial di?erential equation form, leading to the wave equation, the heat equation, the equations of elasticity, the Euler and Navier–Stokes equations for ?uids, the Maxwell equations of electro-magnetics, etc. It is in order to solve ‘constructively’ the heat equation that Fourier developed the series bearing his name in the early 19th century; Fourier series (and later integrals) have played (and still play) a fundamental roleinbothpureandappliedmathematics,includingmanyareasquiteremote from partial di?erential equations. On the other hand, several areas of mathematics such as di?erential ge- etry have bene?ted from their interactions with partial di?erential equations.

Author : Olaf Kolditz
Publisher : Springer Science & Business Media
Page : 382 pages
File Size : 44,6 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9783662047613

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Computational Methods in Environmental Fluid Mechanics by Olaf Kolditz Pdf

Fluids play an important role in environmental systems appearing as surface water in rivers, lakes, and coastal regions or in the subsurface as well as in the atmosphere. Mechanics of environmental fluids is concerned with fluid motion, associated mass and heat transport as well as deformation processes in subsurface systems. In this reference work the fundamental modelling approaches based on continuum mechanics for fluids in the environment are described, including porous media and turbulence. Numerical methods for solving the process governing equations as well as its object-oriented computer implementation are discussed and illustrated with examples. Finally, the application of computer models in civil and environmental engineering is demonstrated.

Author : Johannes Kraus,Ulrich Langer
Publisher : Walter de Gruyter
Page : 241 pages
File Size : 44,7 Mb
Release : 2011-12-22
Category : Mathematics
ISBN : 9783110927092

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Lectures on Advanced Computational Methods in Mechanics by Johannes Kraus,Ulrich Langer Pdf

This book contains four survey papers related to different topics in computational mechanics, in particular (1) novel discretization and solver techniques in mechanics and (2) inverse, control, and optimization problems in mechanics. These topics were considered in lectures, seminars, tutorials, and workshops at the Special Semester on Computational Mechanics held at the Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, in December 2005.

Author : S. P. Venkateshan,Prasanna Swaminathan
Publisher : Springer Nature
Page : 824 pages
File Size : 55,7 Mb
Release : 2023-05-31
Category : Technology & Engineering
ISBN : 9783031082269

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Computational Methods in Engineering by S. P. Venkateshan,Prasanna Swaminathan Pdf

The book is designed to serve as a textbook for courses offered to graduate and upper-undergraduate students enrolled in mechanical engineering. The book attempts to make students with mathematical backgrounds comfortable with numerical methods. The book also serves as a handy reference for practicing engineers who are interested in applications. The book is written in an easy-to-understand manner, with the essence of each numerical method clearly stated. This makes it easy for professional engineers, students, and early career researchers to follow the material presented in the book. The structure of the book has been modeled accordingly. It is divided into four modules: i) solution of a system of equations and eigenvalues which includes linear equations, determining eigenvalues, and solution of nonlinear equations; ii) function approximations: interpolation, data fit, numerical differentiation, and numerical integration; iii) solution of ordinary differential equations—initial value problems and boundary value problems; and iv) solution of partial differential equations—parabolic, elliptic, and hyperbolic PDEs. Each section of the book includes exercises to reinforce the concepts, and problems have been added at the end of each chapter. Exercise problems may be solved by using computational tools such as scientific calculators, spreadsheet programs, and MATLAB codes. The detailed coverage and pedagogical tools make this an ideal textbook for students, early career researchers, and professionals.

Author : Gianluigi Rozza
Publisher : Springer Nature
Page : 180 pages
File Size : 49,9 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9783031498923

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Real Time Reduced Order Computational Mechanics by Gianluigi Rozza Pdf

Author : Bernd Simeon
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 50,9 Mb
Release : 2013-06-14
Category : Mathematics
ISBN : 9783642351587

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Computational Flexible Multibody Dynamics by Bernd Simeon Pdf

This monograph, written from a numerical analysis perspective, aims to provide a comprehensive treatment of both the mathematical framework and the numerical methods for flexible multibody dynamics. Not only is this field permanently and rapidly growing, with various applications in aerospace engineering, biomechanics, robotics, and vehicle analysis, its foundations can also be built on reasonably established mathematical models. Regarding actual computations, great strides have been made over the last two decades, as sophisticated software packages are now capable of simulating highly complex structures with rigid and deformable components. The approach used in this book should benefit graduate students and scientists working in computational mechanics and related disciplines as well as those interested in time-dependent partial differential equations and heterogeneous problems with multiple time scales. Additionally, a number of open issues at the frontiers of research are addressed by taking a differential-algebraic approach and extending it to the notion of transient saddle point problems.

Author : Sandip Mazumder
Publisher : Academic Press
Page : 484 pages
File Size : 40,9 Mb
Release : 2015-12-01
Category : Technology & Engineering
ISBN : 9780128035047

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Numerical Methods for Partial Differential Equations by Sandip Mazumder Pdf

Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary, and initial conditions, and other factors. These two methods have been traditionally used to solve problems involving fluid flow. For practical reasons, the finite element method, used more often for solving problems in solid mechanics, and covered extensively in various other texts, has been excluded. The book is intended for beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful. The material is meant to serve as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics. The notations, language, and technical jargon used in the book can be easily understood by scientists and engineers who may not have had graduate-level applied mathematics or computer science courses. Presents one of the few available resources that comprehensively describes and demonstrates the finite volume method for unstructured mesh used frequently by practicing code developers in industry Includes step-by-step algorithms and code snippets in each chapter that enables the reader to make the transition from equations on the page to working codes Includes 51 worked out examples that comprehensively demonstrate important mathematical steps, algorithms, and coding practices required to numerically solve PDEs, as well as how to interpret the results from both physical and mathematic perspectives

Author : Sören Bartels
Publisher : Springer
Page : 394 pages
File Size : 40,8 Mb
Release : 2015-01-19
Category : Mathematics
ISBN : 9783319137971

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Numerical Methods for Nonlinear Partial Differential Equations by Sören Bartels Pdf

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

Author : William F. Ames
Publisher : Academic Press
Page : 380 pages
File Size : 43,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483262420

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Numerical Methods for Partial Differential Equations by William F. Ames Pdf

Numerical Methods for Partial Differential Equations, Second Edition deals with the use of numerical methods to solve partial differential equations. In addition to numerical fluid mechanics, hopscotch and other explicit-implicit methods are also considered, along with Monte Carlo techniques, lines, fast Fourier transform, and fractional steps methods. Comprised of six chapters, this volume begins with an introduction to numerical calculation, paying particular attention to the classification of equations and physical problems, asymptotics, discrete methods, and dimensionless forms. Subsequent chapters focus on parabolic and hyperbolic equations, elliptic equations, and special topics ranging from singularities and shocks to Navier-Stokes equations and Monte Carlo methods. The final chapter discuss the general concepts of weighted residuals, with emphasis on orthogonal collocation and the Bubnov-Galerkin method. The latter procedure is used to introduce finite elements. This book should be a valuable resource for students and practitioners in the fields of computer science and applied mathematics.