Download or read book Development of an Adaptive Hp Version Finite Element Method for Computational Optimal Control written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-02 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this research effort, the usefulness of hp-version finite elements and adaptive solution-refinement techniques in generating numerical solutions to optimal control problems has been investigated. Under NAG-939, a general FORTRAN code was developed which approximated solutions to optimal control problems with control constraints and state constraints. Within that methodology, to get high-order accuracy in solutions, the finite element mesh would have to be refined repeatedly through bisection of the entire mesh in a given phase. In the current research effort, the order of the shape functions in each element has been made a variable, giving more flexibility in error reduction and smoothing. Similarly, individual elements can each be subdivided into many pieces, depending on the local error indicator, while other parts of the mesh remain coarsely discretized. The problem remains to reduce and smooth the error while still keeping computational effort reasonable enough to calculate time histories in a short enough time for on-board applications. Hodges, Dewey H. and Warner, Michael S. Unspecified Center NAG1-1435...

Download or read book Development of an Hp Version Finite Element Method for Computational Optimal Control written by National Aeronautics and Space Adm Nasa and published by Independently Published. This book was released on 2018-12-29 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this research effort was to begin the study of the application of hp-version finite elements to the numerical solution of optimal control problems. Under NAG-939, the hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element. One possible drawback is the increased computational effort within each element required in implementing hp-version finite elements. We are trying to determine whether this computational effort is sufficiently offset by the reduction in the number of time elements used and improved Newton-Raphson convergence so as to be useful in solving optimal control problems in real time. Because certain of the element interior unknowns can be eliminated at the element level by solving a small set of nonlinear algebraic equations in which the nodal values are taken as given, the scheme may turn out to be especially powerful in a parallel computing environment. A different processor could be assigned to each element. The number of processors, strictly speaking, is not required to be any larger than the number of sub-regions which are free of discontinuities of any kind. Hodges, Dewey H. and Warner, Michael S. NASA-CR-192220, NAS 1.26:192220 NAG1-1435...

Download or read book Development of an Hp version Finite Element for Computional Optimal Control written by Dewey H. Hodges and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Adaptive Finite Element Methods written by Wenbin Liu and published by Alpha Science International Limited. This book was released on 2012 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summary: "This book emphasizes the discussions of some unique issues from the adaptive finite element approximation of optimal control. The main idea used in the approximation error analysis (both a priori and a posteriori) is to first combine convex analysis and interpolation error estimations of suitable interpolators, which much depend on the structure of the control constraints, to derive the error estimates for the control via the variational inequalities in the optimality conditions, and then to apply the standard techniques to derive the error estimates for the state equations. The need, the framework and the techniques of using multi adaptive meshes in developing efficient numerical algorithms for optimal control have been emphasized throughout the book. The book starts from several typical examples of optimal control problems and then discusses existence and optimality conditions for some optimal control problems. It is believed that these discussions are especially useful for the researchers and students who first entered this area. Then the finite element approximation schemes for several typical optimal control problems are set up, their a priori and a posteriori error estimates are derived following the main idea mentioned, and their computational methods are studied."-- Publisher website, viewed 13th July, 2012.

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1989 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 426 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 A Scalable Hp adaptive Finite Element Software with Applications in Fiber Optics written by Stefan Klaus Wilhelm Henneking and published by . This book was released on 2021 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we present a scalable parallel version of hp3D—a finite element (FE) software for analysis and discretization of complex three-dimensional multiphysics applications. The developed software supports hybrid MPI/OpenMP parallelism for large-scale computation on modern manycore architectures. The focus of the effort lies on the development and optimization of the parallel software infrastructure underlying all distributed computation. We discuss the challenges of designing efficient data structures for isotropic and anisotropic hp-adaptive meshes with tetrahedral, hexahedral, prismatic, and pyramidal elements supporting discretization of the exact sequence energy spaces. While the code supports standard Galerkin methods, special emphasis is given to systems arising from discretization with the discontinuous Petrov–Galerkin (DPG) method. The method guarantees discrete stability by employing locally optimal test functions, and it has a built-in error indicator which we exploit to guide mesh adaptivity. In addition to interfacing with third-party packages for various tasks, we have developed our own tools including a parallel nested dissection solver suitable for scalable FE computation of waveguide geometries. We present weak-scaling results with up to 24576 CPU cores and numerical simulations with more than one billion degrees of freedom. The new software capabilities enable solution of challenging wave propagation problems with important applications in acoustics, elastodynamics, and electromagnetics. These applications are difficult to solve in the high-frequency regime because the FE discretization suffers from significant numerical pollution errors that increase with the wavenumber. It is critical to control these errors to obtain a stable and accurate method. We study the pollution effect for waveguide problems with more than 8000 wavelengths in the context of robust DPG FE discretizations for the time-harmonic Maxwell equations. We also discuss adaptive refinement strategies for multi-mode fiber waveguides where the propagating transverse modes must be resolved sufficiently. Our study shows the applicability of the DPG error indicator to this class of problems. Finally, we present both modeling and computational advancements to a unique three-dimensional DPG FE model for the simulation of laser amplification in a fiber amplifier. Fiber laser amplifiers are of interest in communication technology, medical applications, military defense capabilities, and various other fields. Silica fiber amplifiers can achieve high-power operation with great efficiency. At high optical intensities, multi-mode amplifiers suffer from undesired thermal coupling effects which pose a major obstacle in power-scaling of such devices. Our nonlinear 3D vectorial model is based on the time-harmonic Maxwell equations, and it incorporates both amplification via an active dopant and thermal effects via coupling with the heat equation. The model supports co-, counter-, and bi-directional pumping configurations, as well as inhomogeneous and anisotropic material properties. The high-fidelity simulation comes at the cost of a high-order FE discretization with many degrees of freedom per wavelength. To make the computation more feasible, we have developed a novel longitudinal model rescaling, using artificial material parameters with the goal of preserving certain quantities of interest. Numerical tests demonstrate the applicability and utility of this scaled model in the simulation of an ytterbium-doped, step-index fiber amplifier that experiences laser amplification and heating

Download or read book Computing with hp ADAPTIVE FINITE ELEMENTS written by Leszek Demkowicz and published by CRC Press. This book was released on 2006-10-25 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offering the only existing finite element (FE) codes for Maxwell equations that support hp refinements on irregular meshes, Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume 1. One- and Two-Dimensional Elliptic and Maxwell Problems presents 1D and 2D codes and automatic hp adaptivity. This self-contained source discusses the theory and implementat

Download or read book Monthly Catalog of United States Government Publications written by and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computational techniques for adaptive hp finite element methods written by Abani Patra and published by . This book was released on 1996 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Adaptive Finite Element Methods for Differential Equations written by Wolfgang Bangerth and published by Springer Science & Business Media. This book was released on 2003-01-23 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual 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. At the end of each chapter some exercises are posed in order to assist the interested reader in better understanding the concepts presented. Solutions and accompanying remarks are given in the Appendix.

Download or read book Design of Adaptive Finite Element Software written by Alfred Schmidt and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last years, scientific computing has become an important research branch located between applied mathematics and applied sciences and engineering. Highly efficient numerical methods are based on adaptive methods, higher order discretizations, fast linear and non-linear iterative solvers, multi-level algorithms, etc. Such methods are integrated in the adaptive finite element software ALBERTA. It is a toolbox for the fast and flexible implementation of efficient software for real life applications, based on modern algorithms. ALBERTA also serves as an environment for improving existent, or developing new numerical methods in an interplay with mathematical analysis and it allows the direct integration of such new or improved methods in existing simulation software.

Download or read book The Theory and Practice of the H p Version of Finite Element Method written by Ben Q. Guo and published by . This book was released on 1987 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are three versions of finite element method. The classical h-version achieves the accuracy by refining the mesh while using low degrees P of elements, p=1,2 usually. The p-version keep the mesh fixed and the accuracy is achieved by increasing the degree p. The h-p version properly combines both approaches. The h-p version is the new development of finite element method. It was first addressed by Babuska and Dorr?4 . The further analysis and computation for two dimensional problems were made by Guo, Babuska where the exponential rate of convergence was proved. The one dimensional analysis was given by Guo Babuska. The improvement of the results for curvilinear boundary and curvilinear elements was made by Babuska, Guo. The problem with non-homogeneous Dirichlet data was studied by Babuska, Guo. The h-p version with elements for the problem of 2m order was discussed by Guo. The feedback and adaptive approach was developed by Guo, Babuska and Babuska, Rank. This paper is addressing some theoretical advances and presents numerical illustrations.

Download or read book Theoretical Experimental and Numerical Contributions to the Mechanics of Fluids and Solids written by James Casey and published by Birkhäuser. This book was released on 2012-12-06 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: This special issue of ZAMP is published to honor Paul M. Naghdi for his contributions to mechanics over the last forty years and more. It is offered in celebration of his long, productive career in continuum mechan ics; a career which has been marked by a passion for the intrinsic beauty of the subject, an uncompromising adherence to academic standards, and an untiring devotion to our profession. Originally, this issue was planned in celebration of Naghdi's 70th birthday, which occurred on 29 March 1994. But, as the papers were being prepared for the press, it became evident that the illness from which Professor Naghdi had been suffering during recent months was extremely serious. On 26 May 1994, a reception took place in the Department of Mechanical Engineering at Berkeley, at which Naghdi received The Berkeley Citation (which is given in lieu of an honorary degree) and where he was also presented with the Table of Contents of the present collection. Subse quently, he had the opportunity to read the papers in manuscript form. He was very touched that his colleagues had chosen to honor him with their fine contributions. The knowledge that he was held in such high esteem by his fellow scientists brought a special pleasure and consolation to him in his last weeks. On Saturday evening, 9 July 1994, Paul Naghdi succumbed to the lung cancer which he had so courageously endured.

Download or read book Government Reports Announcements Index written by and published by . This book was released on 1995-07 with total page 1164 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Adaptive Finite Element Method for Nonlinear Optimal Control Problems written by Karin Kraft and published by . This book was released on 2011 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: