Download or read book Finite Element Solution to the Helmholtz Equation with High Wave Number Part 2 The H p Version of the FEM written by and published by . This book was released on 1994 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, which is part 2 in a series of two, the investigation of the Galerkin finite element solution to the Helmholtz equation is continued. While part 1 contained results on the h-version with piecewise linear approximation, the present part deals with approximation spaces of order p greater than or equal 1. The method is assumed to be uniform both w.r. to h and p. The results are presented on a one-dimensional model problem with Dirichlet/Robin boundary conditions. In particular there are proven stability estimates, both w.r. to data of higher regularity and data that is bounded in lower norms. (AN).
Download or read book Advanced Finite Element Methods with Applications written by Thomas Apel and published by Springer. This book was released on 2019-06-28 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.
Download or read book Finite Element Solution to the Helmholtz Equation with High Wave Number Part 1 The H Version of the FEM written by and published by . This book was released on 1993 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: The h-version of the finite element method with piecewise linear approximation has been applied to solve a one-dimensional model problem for the Helmholtz equation. The main practical purpose of the investigation is to lay theoretical ground for safe rules of the thumb how to choose the mesh width of the FE-model depending on the wavenumber. In this context we present new results for stability and error estimation of the FE-solution. Following the analysis, numerical results are discussed. In a second paper we will study the h-p-method for Helmholtz problems.
Download or read book Numerical Analysis of Multiscale Problems written by Ivan G. Graham and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 91st London Mathematical Society Durham Symposium took place from July 5th to 15th 2010, with more than 100 international participants attending. The Symposium focused on Numerical Analysis of Multiscale Problems and this book contains 10 invited articles from some of the meeting's key speakers, covering a range of topics of contemporary interest in this area. Articles cover the analysis of forward and inverse PDE problems in heterogeneous media, high-frequency wave propagation, atomistic-continuum modeling and high-dimensional problems arising in modeling uncertainty. Novel upscaling and preconditioning techniques, as well as applications to turbulent multi-phase flow, and to problems of current interest in materials science are all addressed. As such this book presents the current state-of-the-art in the numerical analysis of multiscale problems and will be of interest to both practitioners and mathematicians working in those fields.
Download or read book Maxwell s Equations written by Ulrich Langer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-07-08 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects longer articles on the analysis and numerics of Maxwell’s equations. The topics include functional analytic and Hilbert space methods, compact embeddings, solution theories and asymptotics, electromagnetostatics, time-harmonic Maxwell’s equations, time-dependent Maxwell’s equations, eddy current approximations, scattering and radiation problems, inverse problems, finite element methods, boundary element methods, and isogeometric analysis.
Download or read book High Order Finite Elements for Microsystems Simulation written by Muhammad Razi Abdul Rahman and published by Cuvillier Verlag. This book was released on 2008 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations written by Tarek Mathew and published by Springer Science & Business Media. This book was released on 2008-06-25 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.
Download or read book Domain Decomposition Methods in Science and Engineering XX written by Randolph Bank and published by Springer Science & Business Media. This book was released on 2013-07-03 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the proceedings of the 20th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linearor nonlinear systems of algebraic equations that arise when various problems in continuum mechanics are discretized using finite elements. They are designed for massively parallel computers and take the memory hierarchy of such systems in mind. This is essential for approaching peak floating point performance. There is an increasingly well developed theory whichis having a direct impact on the development and improvements of these algorithms.
Download or read book Spectral Methods written by Jie Shen and published by Springer Science & Business Media. This book was released on 2011-08-25 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.
Download or read book Domain Decomposition Methods Algorithms and Theory written by Andrea Toselli and published by Springer Science & Business Media. This book was released on 2006-06-20 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.
Download or read book Computational Science and Its Applications ICCSA 2003 written by Vipin Kumar and published by Springer Science & Business Media. This book was released on 2003-05-08 with total page 976 pages. Available in PDF, EPUB and Kindle. Book excerpt: The three-volume set, LNCS 2667, LNCS 2668, and LNCS 2669, constitutes the refereed proceedings of the International Conference on Computational Science and Its Applications, ICCSA 2003, held in Montreal, Canada, in May 2003. The three volumes present more than 300 papers and span the whole range of computational science from foundational issues in computer science and mathematics to advanced applications in virtually all sciences making use of computational techniques. The proceedings give a unique account of recent results in computational science.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Download or read book Advances in Structural Vibration written by Subashisa Dutta and published by Springer Nature. This book was released on 2020-10-11 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of selected and peer-reviewed papers presented at the 13th International Conference on Vibration Problems (ICOVP 2017). The topics covered in this book include different structural vibration problems such as dynamics and stability under normal and seismic loading, and wave propagation. The book also discusses different materials such as composite, piezoelectric, and functionally graded materials for improving the stiffness and damping properties of structures. The contents of this book can be useful for beginners, researchers and professionals interested in structural vibration and other allied fields.
Download or read book Computational Acoustics of Noise Propagation in Fluids Finite and Boundary Element Methods written by Steffen Marburg and published by Springer Science & Business Media. This book was released on 2008-02-27 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a survey of numerical methods for acoustics, namely the finite element method (FEM) and the boundary element method (BEM). It is the first book summarizing FEM and BEM (and optimization) for acoustics. The book shows that both methods can be effectively used for many other cases, FEM even for open domains and BEM for closed ones. Emphasis of the book is put on numerical aspects and on treatment of the exterior problem in acoustics, i.e. noise radiation.
Download or read book A Generalized Finite Element Method for Solving the Helmholtz Equation in Two Dimensions with Minimal Pollution written by and published by . This book was released on 1994 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: When using the Galerkin FEM for solving the Helmholtz equation in two dimensions, the error of the corresponding solution differs substantially from the error of the best approximation, and this effect increases with higher wave number k. In this paper we will design a Generalized Finite Element Method (GFEM) for the Helmholtz equation such that the pollution effect is minimal. (AN).
Download or read book Encyclopedia of Computational Mechanics written by Erwin Stein and published by . This book was released on 2004 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopedia of Computational Mechanics provides a comprehensive collection of knowledge about the theory and practice of computational mechanics.
Download or read book Computer Methods in Mechanics written by Mieczyslaw Kuczma and published by Springer Science & Business Media. This book was released on 2010-03-10 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Prominent scientists present the latest achievements in computational methods and mechanics in this book. These lectures were held at the CMM 2009 conference.
