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Book Issues in Applied Mathematics 2013 Edition

Download or read book Issues in Applied Mathematics 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Applied Mathematics / 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Mathematical Physics. The editors have built Issues in Applied Mathematics: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Mathematical Physics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Applied Mathematics: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Book Adaptive Finite Element Methods for Differential Equations

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.

Book Finite Element Methods for Eigenvalue Problems

Download or read book Finite Element Methods for Eigenvalue Problems written by Jiguang Sun and published by CRC Press. This book was released on 2016-08-19 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers finite element methods for several typical eigenvalues that arise from science and engineering. Both theory and implementation are covered in depth at the graduate level. The background for typical eigenvalue problems is included along with functional analysis tools, finite element discretization methods, convergence analysis, techniques for matrix evaluation problems, and computer implementation. The book also presents new methods, such as the discontinuous Galerkin method, and new problems, such as the transmission eigenvalue problem.

Book Inexact Adaptive Finite Element Methods for Elliptic PDE Eigenvalue Problems

Download or read book Inexact Adaptive Finite Element Methods for Elliptic PDE Eigenvalue Problems written by and published by . This book was released on 2011 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book The Finite Element Method for Elliptic Problems

Download or read book The Finite Element Method for Elliptic Problems written by P.G. Ciarlet and published by Elsevier. This book was released on 1978-01-01 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and French universities. For example, it is the author's experience that a one-semester course (on a three-hour per week basis) can be taught from Chapters 1, 2 and 3 (with the exception of Section 3.3), while another one-semester course can be taught from Chapters 4 and 6. On the other hand, it is hoped that this book will prove to be useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. In this respect, Section 3.3, Chapters 5, 7 and 8, and the sections on "Additional Bibliography and Comments should provide many suggestions for conducting seminars.

Book Finite Element Modeling Methods for Photonics

Download or read book Finite Element Modeling Methods for Photonics written by B. M. Azizur Rahman and published by Artech House. This book was released on 2013-08-01 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term photonics can be used loosely to refer to a vast array of components, devices, and technologies that in some way involve manipulation of light. One of the most powerful numerical approaches available to engineers developing photonic components and devices is the Finite Element Method (FEM), which can be used to model and simulate such components/devices and analyze how they will behave in response to various outside influences. This resource provides a comprehensive description of the formulation and applications of FEM in photonics applications ranging from telecommunications, astronomy, and sensing, to chemistry, imaging, and biomedical R&D. This book emphasizes practical, problem-solving applications and includes real-world examples to assist readers in understanding how mathematical concepts translate to computer code for finite element-based methods applicable to a range of photonic structures. In addition, this is the perfect support to anyone using the COMSOL Multiphysics© RF Module.

Book Discontinuous Hp Finite Element Methods for Elliptic Eigenvalue Problems with Singular Potentials

Download or read book Discontinuous Hp Finite Element Methods for Elliptic Eigenvalue Problems with Singular Potentials written by Carlo Marcati and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study elliptic eigenvalue problems with singular potentials, motivated by several models in physics and quantum chemistry, and we propose a discontinuous Galerkin hp finite element method for their solution. In these models, singular potentials occur naturally (associated with the interaction between nuclei and electrons). Our analysis starts from elliptic regularity in non homogeneous weighted Sobolev spaces. We show that elliptic operators with singular potential are isomorphisms in those spaces and that we can derive weighted analytic type estimates on the solutions to the linear eigenvalue problems. The isotropically graded hp method provides therefore approximations that converge with exponential rate to the solution of those eigenproblems. We then consider a wide class of nonlinear eigenvalue problems, and prove the convergence of numerical solutions obtained with the symmetric interior penalty discontinuous Galerkin method. Furthermore, when the non linearity is polynomial, we show that we can obtain the same analytic type estimates as in the linear case, thus the numerical approximation converges exponentially. We also analyze under what conditions the eigenvalue converges at an increased rate compared to the eigenfunctions. For both the linear and nonlinear case, we perform numerical tests whose objective is both to validate the theoretical results, but also evaluate the role of sources of errors not considered previously in the analysis, and to help in the design of hp/dG graded methods for more complex problems.

Book Adaptive Finite Elements in the Discretization of Parabolic Problems

Download or read book Adaptive Finite Elements in the Discretization of Parabolic Problems written by Christian A. Möller and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adaptivity is a crucial tool in state-of-the-art scientific computing. However, its theoretical foundations are only understood partially and are subject of current research. This self-contained work provides theoretical basics on partial differential equations and finite element discretizations before focusing on adaptive finite element methods for time dependent problems. In this context, aspects of temporal adaptivity and error control are considered in particular. Based on the gained insights, a specific adaptive algorithm is designed and analyzed thoroughly. Most importantly, it is proven that the presented adaptive method terminates within any demanded error tolerance. Moreover, the developed algorithm is analyzed from a numerical point of view and its performance is compared to well-known standard methods. Finally, it is applied to the real-life problem of concrete carbonation, where two different discretizations are compared.

Book Scientific Computing in Electrical Engineering

Download or read book Scientific Computing in Electrical Engineering written by Angelo Marcello Anile and published by Springer Science & Business Media. This book was released on 2007-01-10 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers presented at the last Scientific Computing in Electrical Engineering (SCEE) Conference, held in Sicily, in 2004. The series of SCEE conferences aims at addressing mathematical problems which have a relevancy to industry. The areas covered at SCEE-2004 were: Electromagnetism, Circuit Simulation, Coupled Problems and General mathematical and computational methods.

Book Convergence of Adaptive Finite Element Methods for Semi Linear Elliptic Partial Differential Equations

Download or read book Convergence of Adaptive Finite Element Methods for Semi Linear Elliptic Partial Differential Equations written by Thanatyod Jampawai and published by . This book was released on 2014 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze a standard adaptive finite element method (AFEM) for second order semi-linear elliptic partial differential equations with vanishing boundary over a polygonal domain in R^{2}. We prove a contraction property for the weighted sum of the energy error and the error estimator between any two consecutive loops, which implies the convergence of AFEM. The result is obtained based on the assumptions that the initial triangulation is sufficiently refined and a Lipschitz constant is sufficiently small in order to deal with the nonlinear inhomogeneous term f(x, u(x)), which is also assumed to be Lipschitz in the second variable.

Book Convergence of Goal oriented Adaptive Finite Element Methods

Download or read book Convergence of Goal oriented Adaptive Finite Element Methods written by Sara Pollock and published by . This book was released on 2012 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we discuss convergence theory for goal-oriented adaptive finite element methods for second order elliptic problems. We develop results for both linear nonsymmetric and semilinear problems. We start with a brief description of the finite element method applied to these problems and some basic error estimates. We then provide a detailed error analysis of the method as described for each problem. In each case, we establish convergence in the sense of the quantity of interest with a goal-oriented variation of the standard adaptive finite element method using residual-based indicators. In the linear case we establish the adjoint as the appropriate differential operator for the dual problem. We establish contraction of the quasi-error for each of the primal and dual problems yielding convergence in the quantity of interest. We follow these results with a complexity analysis of the method. In the semilinear case we introduce three types of linearized dual problems used to establish our results. We give a brief summary of a priori estimates for this class of problems. After establishing contraction results for the primal problem, we then provide additional estimates to show contraction of the combined primal and dual system, yielding convergence of the goal function. We support these results with some numerical experiments. Finally, we include an appendix outlining some common methods used in a posteriori error estimation and briefly describe iterative methods for solving nonlinear problems.

Book Adaptive Finite Element Method for Eigenvalue Problems

Download or read book Adaptive Finite Element Method for Eigenvalue Problems written by Corina Spreiter and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: