Finite Elements And Fast Iterative Solvers With Applications In Incompressible Fluid Dynamics
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Finite Elements And Fast Iterative Solvers With Applications In Incompressible Fluid Dynamics
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Author : Howard C. Elman
language : en
Publisher: OUP Oxford
Release Date : 2005-05-19
Finite Elements And Fast Iterative Solvers With Applications In Incompressible Fluid Dynamics written by Howard C. Elman and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-19 with Computers categories.
The authors' intended audience is at the level of graduate students and researchers, and we believe that the text offers a valuable contribution to all finite element researchers who would like to broadened both their fundamental and applied knowledge of the field. - Spencer J. Sherwin and Robert M. Kirby, Fluid Mechanics, Vol 557, 2006.
Finite Elements And Fast Iterative Solvers
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Author : Howard C. Elman
language : en
Publisher: Oxford University Press
Release Date : 2014
Finite Elements And Fast Iterative Solvers written by Howard C. Elman and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Mathematics categories.
A practical graduate text on Scientific Computing with a focus on numerical solution of partial differential equations and numerical linear algebra. This book, and its associated freely downloadable MATLAB software, is relevant to engineers, applied mathematicians, numerical analysts, and people working in interdisciplinary Scientific Computing.
Finite Elements And Fast Iterative Solvers
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Author : Howard Elman
language : en
Publisher: OUP Oxford
Release Date : 2014-06-19
Finite Elements And Fast Iterative Solvers written by Howard Elman and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-19 with Mathematics categories.
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.
The Finite Volume Method In Computational Fluid Dynamics
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Author : F. Moukalled
language : en
Publisher: Springer
Release Date : 2015-08-13
The Finite Volume Method In Computational Fluid Dynamics written by F. Moukalled and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-13 with Technology & Engineering categories.
This textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within Matlab. The second is OpenFOAM®, an open source framework used in the development of a range of CFD programs for the simulation of industrial scale flow problems. With over 220 figures, numerous examples and more than one hundred exercise on FVM numerics, programming, and applications, this textbook is suitable for use in an introductory course on the FVM, in an advanced course on numerics, and as a reference for CFD programmers and researchers.
Mixed Finite Element Methods And Applications
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Author : Daniele Boffi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-02
Mixed Finite Element Methods And Applications written by Daniele Boffi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-02 with Mathematics categories.
Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem, plate problems, elasticity and electromagnetism.
The Finite Element Method In Heat Transfer And Fluid Dynamics
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Author : J. N. Reddy
language : en
Publisher: CRC Press
Release Date : 2010-04-06
The Finite Element Method In Heat Transfer And Fluid Dynamics written by J. N. Reddy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-06 with Science categories.
As Computational Fluid Dynamics (CFD) and Computational Heat Transfer (CHT) evolve and become increasingly important in standard engineering design and analysis practice, users require a solid understanding of mechanics and numerical methods to make optimal use of available software. Considered to be among the very best in the field, this masterwork from renowned experts J. N. Reddy and D. K. Gartling is the latest version of a book that has long been relied upon by practicing engineers, researchers, and graduate students. Noted for its powerful methodology and clear explanations of the subject, this third edition contains considerably more workable exercises and examples associated with problems in heat conduction, incompressible viscous flow, and convection heat transfer. It also uses applied examples to illustrate applications of FEM in thermal and fluid design analysis.
Finite Element Methods For Navier Stokes Equations
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Author : Vivette Girault
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Finite Element Methods For Navier Stokes Equations written by Vivette Girault and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The material covered by this book has been taught by one of the authors in a post-graduate course on Numerical Analysis at the University Pierre et Marie Curie of Paris. It is an extended version of a previous text (cf. Girault & Raviart [32J) published in 1979 by Springer-Verlag in its series: Lecture Notes in Mathematics. In the last decade, many engineers and mathematicians have concentrated their efforts on the finite element solution of the Navier-Stokes equations for incompressible flows. The purpose of this book is to provide a fairly comprehen sive treatment of the most recent developments in that field. To stay within reasonable bounds, we have restricted ourselves to the case of stationary prob lems although the time-dependent problems are of fundamental importance. This topic is currently evolving rapidly and we feel that it deserves to be covered by another specialized monograph. We have tried, to the best of our ability, to present a fairly exhaustive treatment of the finite element methods for inner flows. On the other hand however, we have entirely left out the subject of exterior problems which involve radically different techniques, both from a theoretical and from a practical point of view. Also, we have neither discussed the implemen tation of the finite element methods presented by this book, nor given any explicit numerical result. This field is extensively covered by Peyret & Taylor [64J and Thomasset [82].
The Finite Element Method Theory Implementation And Applications
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Author : Mats G. Larson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-13
The Finite Element Method Theory Implementation And Applications written by Mats G. Larson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-13 with Computers categories.
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.
Automation Of Finite Element Methods
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Author : Jože Korelc
language : en
Publisher: Springer
Release Date : 2016-06-08
Automation Of Finite Element Methods written by Jože Korelc and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-08 with Technology & Engineering categories.
New finite elements are needed as well in research as in industry environments for thedevelopment of virtual prediction techniques. The design and implementation of novel finiteelements for specific purposes is a tedious and time consuming task, especially for nonlinearformulations. The automation of this process can help to speed up this processconsiderably since the generation of the final computer code can be accelerated by order ofseveral magnitudes.This book provides the reader with the required knowledge needed to employ modernautomatic tools like AceGen within solid mechanics in a successful way. It covers the rangefrom the theoretical background, algorithmic treatments to many different applications. Thebook is written for advanced students in the engineering field and for researchers ineducational and industrial environments.
Modern Fortran Explained
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Author : Michael Metcalf
language : en
Publisher: Oxford University Press
Release Date : 2024-02-16
Modern Fortran Explained written by Michael Metcalf and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-16 with Mathematics categories.
Fortran remains one of the principal programming languages used in high-performance scientific, numerical, and engineering computing. A series of significant revisions to the standard versions of the language have progressively enhanced its capabilities, and the current standard - Fortran 2023 - brings with it further additions and improvements. The language as defined by its most recent standards, with their introduction of object-oriented programming and of coarrays, is often referred to generically as 'Modern Fortran', and this term is increasingly used in the literature. Thus, we see that Fortran's particular advantages as a high-end numerical language, especially where arrays are the main form of data object and/or where complex arithmetic is involved, are still to the fore. It is able to attain the highest achievable optimization, mainly because multi-dimensional arrays are 'natural' objects and because its pointers are highly constrained. There is every sign that Modern Fortran will continue to be used to tackle major scientific computing problems in the next decade and beyond and will long remain a living tribute to its early pioneers. This third edition of Modern Fortran Explained expands on the second. The material contained in the four final chapters of the second edition have been merged into the main text, thereby offering, in 20 chapters, a comprehensive and uniform description of Fortran 2018. The additional features now brought by the 2023 standard, which are mostly relatively minor in nature, are described in two final chapters, the first on generic programming and the second on the other features. This structure enables the reader to distinguish clearly between what is old and what is new. This new edition, written by experts in the field, three of whom have actively contributed to Fortran 2023, is thus a complete and authoritative description of Fortran in its latest form, with the intention that it remain the main reference work in the field.