Numerical Solution of Partial Differential Equations by the Finite Element Method PDF Download
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Author: Claes Johnson
Publisher: Courier Corporation
ISBN: 0486131599
Category : Mathematics
Languages : en
Pages : 290
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Book Description
An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.
Author: Claes Johnson
Publisher: Courier Corporation
ISBN: 0486131599
Category : Mathematics
Languages : en
Pages : 290
Get Book Here
Book Description
An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.
Author: Anders Logg
Publisher: Springer Science & Business Media
ISBN: 3642230997
Category : Computers
Languages : en
Pages : 723
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Book Description
This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
Author: K. K. Ang
Publisher: World Scientific
ISBN: 9789812776228
Category : Technology & Engineering
Languages : en
Pages : 1090
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Book Description
ICSSD 2002 is the second in the series of International Conferences on Structural Stability and Dynamics, which provides a forum for the exchange of ideas and experiences in structural stability and dynamics among academics, engineers, scientists and applied mathematicians. Held in the modern and vibrant city of Singapore, ICSSD 2002 provides a peep at the areas which experts on structural stability and dynamics will be occupied with in the near future. From the technical sessions, it is evident that well-known structural stability and dynamic theories and the computational tools have evolved to an even more advanced stage. Many delegates from diverse lands have contributed to the ICSSD 2002 proceedings, along with the participation of colleagues from the First Asian Workshop on Meshfree Methods and the International Workshop on Recent Advances in Experiments and Computations on Modeling of Heterogeneous Systems. Forming a valuable source for future reference, the proceedings contain 153 papers OCo including 3 keynote papers and 23 invited papers OCo contributed by authors from all over the world who are working in advanced multi-disciplinary areas of research in engineering. All these papers are peer-reviewed, with excellent quality, and cover the topics of structural stability, structural dynamics, computational methods, wave propagation, nonlinear analysis, failure analysis, inverse problems, non-destructive evaluation, smart materials and structures, vibration control and seismic responses.The major features of the book are summarized as follows: a total of 153 papers are included with many of them presenting fresh ideas and new areas of research; all papers have been peer-reviewed and are grouped into sections for easy reference; wide coverage of research areas is provided and yet there is good linkage with the central topic of structural stability and dynamics; the methods discussed include those that are theoretical, analytical, computational, artificial, evolutional and experimental; the applications range from civil to mechanical to geo-mechanical engineering, and even to bioengineering."
Author: Pavel Solin
Publisher: CRC Press
ISBN: 0203488040
Category : Mathematics
Languages : en
Pages : 404
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Book Description
The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and
Author: Randolph Bank
Publisher: Birkhäuser
ISBN: 3034885288
Category : Mathematics
Languages : en
Pages : 314
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Book Description
Progress in today's high-technology industries is strongly associated with the development of new mathematical tools. A typical illustration of this partnership is the mathematical modelling and numerical simulation of electric circuits and semiconductor devices. At the second Oberwolfach conference devoted to this important and timely field, scientists from around the world, mainly applied mathematicians and electrical engineers from industry and universities, presented their new results. Their contributions, forming the body of this work, cover electric circuit simulation, device simulation and process simulation. Discussions on experiences with standard software packages and improvements of such packages are included. In the semiconductor area special lectures were given on new modelling approaches, numerical techniques and existence and uniqueness results. In this connection, mention is made, for example, of mixed finite element methods, an extension of the Baliga-Patankar technique for a three dimensional simulation, and the connection between semiconductor equations and the Boltzmann equations.
Author: F. Thomasset
Publisher: Springer Science & Business Media
ISBN: 3642870473
Category : Science
Languages : en
Pages : 168
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Book Description
In structure mechanics analysis, finite element methods are now well estab lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977». (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients,l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.
Author: Mats G. Larson
Publisher: Springer Science & Business Media
ISBN: 3642332870
Category : Computers
Languages : en
Pages : 403
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Book Description
This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.
Author: Chien Ming Wang
Publisher: World Scientific
ISBN: 9814486825
Category : Technology & Engineering
Languages : en
Pages : 1083
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Book Description
ICSSD 2002 is the second in the series of International Conferences on Structural Stability and Dynamics, which provides a forum for the exchange of ideas and experiences in structural stability and dynamics among academics, engineers, scientists and applied mathematicians. Held in the modern and vibrant city of Singapore, ICSSD 2002 provides a peep at the areas which experts on structural stability and dynamics will be occupied with in the near future. From the technical sessions, it is evident that well-known structural stability and dynamic theories and the computational tools have evolved to an even more advanced stage. Many delegates from diverse lands have contributed to the ICSSD 2002 proceedings, along with the participation of colleagues from the First Asian Workshop on Meshfree Methods and the International Workshop on Recent Advances in Experiments and Computations on Modeling of Heterogeneous Systems. Forming a valuable source for future reference, the proceedings contain 153 papers — including 3 keynote papers and 23 invited papers — contributed by authors from all over the world who are working in advanced multi-disciplinary areas of research in engineering. All these papers are peer-reviewed, with excellent quality, and cover the topics of structural stability, structural dynamics, computational methods, wave propagation, nonlinear analysis, failure analysis, inverse problems, non-destructive evaluation, smart materials and structures, vibration control and seismic responses.The major features of the book are summarized as follows: a total of 153 papers are included with many of them presenting fresh ideas and new areas of research; all papers have been peer-reviewed and are grouped into sections for easy reference; wide coverage of research areas is provided and yet there is good linkage with the central topic of structural stability and dynamics; the methods discussed include those that are theoretical, analytical, computational, artificial, evolutional and experimental; the applications range from civil to mechanical to geo-mechanical engineering, and even to bioengineering.
Author: Howard Elman
Publisher: OUP Oxford
ISBN: 0191667927
Category : Mathematics
Languages : en
Pages : 495
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Book Description
This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory " provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.
Author: Ben Q. Li
Publisher: Springer Science & Business Media
ISBN: 1846282055
Category : Technology & Engineering
Languages : en
Pages : 587
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Book Description
Over the past several years, significant advances have been made in developing the discontinuous Galerkin finite element method for applications in fluid flow and heat transfer. Certain unique features of the method have made it attractive as an alternative for other popular methods such as finite volume and finite elements in thermal fluids engineering analyses. This book is written as an introductory textbook on the discontinuous finite element method for senior undergraduate and graduate students in the area of thermal science and fluid dynamics. It also can be used as a reference book for researchers and engineers who intend to use the method for research in computational fluid dynamics and heat transfer. A good portion of this book has been used in a course for computational fluid dynamics and heat transfer for senior undergraduate and first year graduate students. It also has been used by some graduate students for self-study of the basics of discontinuous finite elements. This monograph assumes that readers have a basic understanding of thermodynamics, fluid mechanics and heat transfer and some background in numerical analysis. Knowledge of continuous finite elements is not necessary but will be helpful. The book covers the application of the method for the simulation of both macroscopic and micro/nanoscale fluid flow and heat transfer phenomena.
