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Wednesday, July 22, 2020 | History

3 edition of Spectral and spectral-element methods found in the catalog.

Spectral and spectral-element methods

Spectral and spectral-element methods

lecture notes in high performance computational physics

  • 66 Want to read
  • 36 Currently reading

Published by National Aeronautics and Space Administration, Goddard Space Flight Center, National Technical Information Service, distributor] in Greenbelt, Md, [Springfield, Va .
Written in English

    Subjects:
  • Fast Fourier transformations.,
  • Numerical analysis.,
  • Spectral methods.,
  • Mathematical models.,
  • Hydrodynamics.

  • Edition Notes

    Other titlesSpectral and spectral element methods, Lecture notes in high performance computational physics
    StatementAnil E. Deane.
    SeriesNASA contractor report -- 203877, NASA contractor report -- NASA CR-203877.
    ContributionsGoddard Space Flight Center.
    The Physical Object
    FormatMicroform
    Pagination1 v.
    ID Numbers
    Open LibraryOL17128441M

    GE – Computational Geophysics The spectral element method Jean-Paul Ampuero∗ Abstract The spectral element method (SEM) is a high order numerical method for solving partial differential equations that inherits the ac-curacy of spectral methods and the geometrical flexibility of File Size: KB.   Incorporating new topics and original material, Introduction to Finite and Spectral Element Methods Using MATLAB ®, Second Edition enables readers to quickly understand the theoretical foundation and practical implementation of the finite element method and its companion spectral element method. Readers gain hands-on computational experience by using the free online FSELIB library of Price: $

    This text provides a hands-on introduction to spectral methods in is built around 40 short and powerful MATLAB programs. Users of this book include advanced undergraduate and graduate students studying numerical methods for PDEs, numerical analysts, engineers, and computationally oriented physical scientists in all areas.   Spectral Element Method in Structural Dynamics is a concise and timely introduction to the spectral element method (SEM) as a means of solving problems in structural dynamics, wave propagations, and other related fields. The book consists of three key sections. In the first part, background knowledge is set up for the readers by reviewing previous work in the area and by Author: Usik Lee.

    Spectral Element: Essentials Weak formulation of the wave equation Transformation to the elemental level (Jacobian) That is the key feature of the spectral element method. Mass and stiffness matrix Definition of the - at this point - global mass matrix Mji = Z G . methods is described and an example of the application of the spectral element method to a second-orderelliptic equation provides the reader a practical information about it. Next, some direct and iterative methods to solve the resulting linear algebraic systems areCited by:


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Spectral and spectral-element methods Download PDF EPUB FB2

Introduction to Finite and Spectral Element Methods Using MATLAB provides a means of quickly understanding both the theoretical foundation and practical implementation of the finite element method and its companion spectral element method.

Written in the form of a self-contained course, it introduces the fundamentals on a need-to-know basis and /5(2). Containing over 50% new material, including discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilisation and filtering techniques, this text aims to introduce a wider audience to the use of spectral/hp element methods with particular emphasis on their application to unstructured meshes.5/5(1).

An excellent source on spectral finite elements (includes code) is the recent book by Pozrikidis: Introduction to Finite and Spectral Element Methods using MATLAB (snippets from the chapters).

The style and content is aligned with that of a textbook and not a research monograph. It provides a very nice transition from finite elements to spectral. We implement all methods, including the semi-implicit Robin based coupling method, in the context of spectral element discretization, which is more sensitive to temporal instabilities than low.

Spectral Element Method in Structural Dynamics is a concise and timely introduction to the spectral element method (SEM) as a means of solving problems in structural dynamics, wave propagations, and other related fields.

The book consists of three key sections. In the first part, background knowledge is set up for the readers by reviewing previous work in the area and by. Traditionally spectral methods in fluid dynamics were used in direct and large eddy simulations of turbulent flow in simply connected computational domains.

The methods are now being applied to more complex geometries, and the spectral/hp element method, which incorporates both multi-domain spectral methods and high-order finite element methods, has been particularly successful.

Spectral methods have long been popular in direct and large eddy simulation of turbulent flows, but their use in areas with complex-geometry computational domains has historically been much more limited. More recently, the need to find accurate solutions to the viscous flow equations around complex configurations has led to the development of high-order discretization procedures on.

2 Spatialdiscretizationofpartialdi erentialequa-tions Introduction Finitevolume, niteelement,spectralandalso nitedi erencemethodsmaybeviewed. Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations, potentially involving the use of the fast Fourier idea is to write the solution of the differential equation as a sum of certain "basis functions" (for example, as a Fourier series which is a sum of sinusoids) and then to choose the.

Applications in Mechanics. Viscous Flow. Finite and Spectral Element Methods in Three Dimensions. Appendices. References.

Index. Abstract: Helps to understand both the theoretical foundation and practical implementation of the finite element method and its companion spectral element method.

Book Description. Incorporating new topics and original material, Introduction to Finite and Spectral Element Methods Using MATLAB ®, Second Edition enables readers to quickly understand the theoretical foundation and practical implementation of the finite element method and its companion spectral element method.

Readers gain hands-on computational experience by using the free online. Spectral methods involve seeking the solution to a differential equation in terms of a series of known, smooth functions. They have recently emerged as a viable alternative to finite difference and finite element methods for the numerical solution of partial differential equations.

Spectral element methods are high-order weighted-residual techniques for partial differential equations that combine the geometric flexibility of finite element techniques with the rapid convergence rate of spectral schemes. The theoretical foundations and numerical implementation of spectral element methods for the incompressible Navier-Stokes equations are presented, considering the Cited by: The spectral-element method is a high-order numerical method that allows us to solve the seismic wave equation in 3D heterogeneous Earth : Andreas Fichtner.

Summary. Incorporating new topics and original material, Introduction to Finite and Spectral Element Methods Using MATLAB ®, Second Edition enables readers to quickly understand the theoretical foundation and practical implementation of the finite element method and its companion spectral element method.

Readers gain hands-on computational experience by using the free online FSELIB library of. The spectral and spectral element discretizations of partial differential equations rely on high degree polynomial approximation and on the use of tensorized bases of polynomials.

Firstly, on a square or a cube, we describe the basic tools for spectral methods, and we prove some optimal properties of polynomial approximation and by: 8. 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 prese. Buy Introduction to Finite and Spectral Element Methods using MATLAB 1 by Pozrikidis, Constantine (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on /5(2). If I go by this paper, spectral element methods are a subset of FEM methods and the only difference lies in the choice of basis functions.

If this is the case, are there any advantages in using traditional FEM based Lagrange basis functions or SEM based on GLL Lagrange basis functions as this leads to dense matrices and bad condition numbers.

: Spectral/hp Element Methods for Computational Fluid Dynamics (Numerical Mathematics and Scientific Computation) () by Karniadakis, George Em; Sherwin, Spencer J. and a great selection of similar New, Used and Collectible Books available now at great prices.5/5(1).

In this work, we proposed a spectral integral method (SIM)-spectral element method (SEM)- finite element method (FEM) domain decomposition method (DDM) for solving inhomogeneous multi-scale problems.

The proposed SIM-SEM-FEM domain decomposition algorithm can efficiently handle problems with multi-scale structures.Get this from a library! Introduction to finite and spectral element methods using MATLAB. [C Pozrikidis] -- Introduction to Finite and Spectral Element Methods using MATLAB provides a means of quickly understanding both the theoretical foundations and practical implementation of the finite method and its.: Introduction to Finite and Spectral Element Methods using MATLAB () by Pozrikidis, Constantine and a great selection of similar New, Used and Collectible Books available now at 5/5(1).