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Author : Imran Haq
Publisher :
ISBN 13 :
Total Pages : 104 pages
Book Rating : 4.:/5 (382 download)
Download or read book Adaptive Finite Element Solutions of the Steady Euler Equations Using a Sensitivity Approach written by Imran Haq and published by . This book was released on 1997 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard A Shapiro
Publisher :
ISBN 13 : 9783322878809
Total Pages : 184 pages
Book Rating : 4.8/5 (788 download)
Download or read book Adaptive Finite Element Solution Algorithm for the Euler Equations written by Richard A Shapiro and published by . This book was released on 2012-03-28 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wolfgang Bangerth
Publisher : Birkhäuser
ISBN 13 : 303487605X
Total Pages : 216 pages
Book Rating : 4.0/5 (348 download)
Download or read book Adaptive Finite Element Methods for Differential Equations written by Wolfgang Bangerth and published by Birkhäuser. This book was released on 2013-11-11 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR method) for goal-oriented error estimation is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.
Author : Richard A. Shapiro
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (11 download)
Download or read book Adaptive Finite Element Methods for the Euler Equations written by Richard A. Shapiro and published by . This book was released on 1989 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard Abraham Shapiro
Publisher :
ISBN 13 :
Total Pages : 862 pages
Book Rating : 4.:/5 (197 download)
Download or read book An Adaptive Finite Element Solution Algorithm for the Euler Equations written by Richard Abraham Shapiro and published by . This book was released on 1988 with total page 862 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard A. Shapiro
Publisher : Vieweg+Teubner Verlag
ISBN 13 : 3322878791
Total Pages : 180 pages
Book Rating : 4.3/5 (228 download)
Download or read book Adaptive Finite Element Solution Algorithm for the Euler Equations written by Richard A. Shapiro and published by Vieweg+Teubner Verlag. This book was released on 2013-03-08 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the result of my PhD thesis work in Computational Fluid Dynamics at the Massachusettes Institute of Technology under the supervision of Professor Earll Murman. A new finite element al gorithm is presented for solving the steady Euler equations describing the flow of an inviscid, compressible, ideal gas. This algorithm uses a finite element spatial discretization coupled with a Runge-Kutta time integration to relax to steady state. It is shown that other algorithms, such as finite difference and finite volume methods, can be derived using finite element principles. A higher-order biquadratic approximation is introduced. Several test problems are computed to verify the algorithms. Adaptive gridding in two and three dimensions using quadrilateral and hexahedral elements is developed and verified. Adaptation is shown to provide CPU savings of a factor of 2 to 16, and biquadratic elements are shown to provide potential savings of a factor of 2 to 6. An analysis of the dispersive properties of several discretization methods for the Euler equations is presented, and results allowing the prediction of dispersive errors are obtained. The adaptive algorithm is applied to the solution of several flows in scramjet inlets in two and three dimensions, demonstrat ing some of the varied physics associated with these flows. Some issues in the design and implementation of adaptive finite element algorithms on vector and parallel computers are discussed.
Author : Ralf Hartmann
Publisher :
ISBN 13 :
Total Pages : 141 pages
Book Rating : 4.:/5 (249 download)
Download or read book Adaptive Finite Element Methods for the Compressible Euler Equations written by Ralf Hartmann and published by . This book was released on 2002 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ekkehard Ramm
Publisher : John Wiley & Sons
ISBN 13 : 0471496502
Total Pages : 436 pages
Book Rating : 4.4/5 (714 download)
Download or read book Error-controlled Adaptive Finite Elements in Solid Mechanics written by Ekkehard Ramm and published by John Wiley & Sons. This book was released on 2002-12-30 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Element Methods are used for numerous engineering applications where numerical solutions of partial differential equations are needed. As computers can now deal with the millions of parameters used in these methods, automatic error estimation and automatic adaptation of the utilised method (according to this error estimation), has become a hot research topic. This text offers comprehensive coverage of this new field of automatic adaptation and error estimation, bringing together the work of eight outstanding researchers in this field who have completed a six year national research project within the German Science Foundation. The result is a state-of-the-art work in true reference style. Each chapter is self-contained and covers theoretical, algorithmic and software presentations as well as solved problems. A main feature consists of several carefully elaborated benchmarks of 2D- and 3D- applications. First book to go beyond the Finite Element Method in itself Covers material from a new research area Presents benchmarks of 2D- and 3D- applications Fits with the new trend for genetic strategies in engineering
Download or read book Adaptive Finite Element Methods for the Compressible Euler Equations written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we introduce a discontinuous Galerkin method for the numerical solution of hyperbolic conversation laws, as for example the compressible Euler equations of gas dynamics. Based on this finite element method, we develop an adaptive algorithm for the efficient computation of physically relevant quantities of the solution. This includes a posteriori error estimation of the error in the computed quantity as well as adaptive mesh design specifically tailored to the efficient computation of this quantity. We illustrate this approach by several different hyperbolic problems in combination with various different target quantities, including the efficient computation of drag and lift coefficients of airfoils immersed in inviscid compressible gas flows.
Author : Murtazo Nazarov
Publisher :
ISBN 13 : 9789174153651
Total Pages : 39 pages
Book Rating : 4.1/5 (536 download)
Download or read book An Adaptive Finite Element Method for the Compressible Euler Equations written by Murtazo Nazarov and published by . This book was released on 2009 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Lisa G. Stanley
Publisher : SIAM
ISBN 13 : 9780898717556
Total Pages : 160 pages
Book Rating : 4.7/5 (175 download)
Download or read book Design Sensitivity Analysis written by Lisa G. Stanley and published by SIAM. This book was released on 2002-01-01 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an understandable introduction to one approach to design sensitivity computation and illustrates some of the important mathematical and computational issues inherent in using the sensitivity equation method (SEM) for partial differential equations. The authors use basic models to illustrate the computational issues that one might encounter when applying the SEM in a laboratory or research setting, while providing an overview of applications and computational issues regarding sensitivity calculations performed by way of continuous sensitivity equation methods (CSEM).
Author : Farzad Taghaddosi
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (11 download)
Download or read book An Adaptive Least-squares Finite Element Method for the Compressible Euler Equations written by Farzad Taghaddosi and published by . This book was released on 1996 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Zhangxin Chen
Publisher : Springer Science & Business Media
ISBN 13 : 3540240780
Total Pages : 415 pages
Book Rating : 4.5/5 (42 download)
Download or read book Finite Element Methods and Their Applications written by Zhangxin Chen and published by Springer Science & Business Media. This book was released on 2005-06-23 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduce every concept in the simplest setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Contains unique recent developments of various finite elements such as nonconforming, mixed, discontinuous, characteristic, and adaptive finite elements, along with their applications. Describes unique recent applications of finite element methods to important fields such as multiphase flows in porous media and semiconductor modelling. Treats the three major types of partial differential equations, i.e., elliptic, parabolic, and hyperbolic equations.
Author : Anders Logg
Publisher : Springer Science & Business Media
ISBN 13 : 3642230997
Total Pages : 723 pages
Book Rating : 4.6/5 (422 download)
Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
Publisher :
ISBN 13 :
Total Pages : 704 pages
Book Rating : 4.:/5 (31 download)
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive Finite Element Methods for Optimization in Partial Differential Equations written by and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to error control and mesh adaptivity is described for the discretization of optimal control problems governed by (elliptic) partial differential equations. The Lagrangian formalism yields the first-order necessary optimality condition in form of an indefinite boundary value problem which is approximated by an adaptive Galerkin finite element method. The mesh design in the resulting reduced models is controlled by residual-based a posteriori error estimates. These are derived by duality arguments employing the cost functional of the optimization problem for controlling the discretization error. In this case, the computed state and co-state variables can be used as sensitivity factors multiplying the local cell-residuals in the error estimators. This results in a generic and efficient algorithm for mesh adaptation within the optimization process. Applications of the developed method are boundary control problem models governed by Ginzburg-Landau equations (superconductivity in semi-conductors), by Navier-Stokes equations, and by the Boussinesq viscosity model (flow with temperature transport for zero gravitation). Computations with more than 2 million unknowns were performed.
Author :
Publisher :
ISBN 13 :
Total Pages : 57 pages
Book Rating : 4.:/5 (227 download)
Download or read book Adaptive Finite Element Method I: Solution Algorithm and Computational Examples written by and published by . This book was released on 1994 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: An adaptive finite element method is developed to solve initial boundary value problems for vector systems of parabolic partial differential equations in one space dimension and time. The differential equations are discretized in space using piecewise linear finite element approximations. Superconvergence properties and quadratic polynomials are used to derive a computation ally inexpensive approximation to the spatial component of the error. This technique is coupled with time integration schemes of successively higher orders to obtain an approximation of the temporal and total discretization errors. These approximate errors are used to control an adaptive mesh refinement strategy. Refinement is performed in space, time, or both space and time depending on the dominant component of the error estimate. A computer code coupling this refinement strategy and stable mesh movement has been written and applied to a number of problems. These computations confirm that proper mesh movement can reduce the computational efforts associated with mesh refinement.
