Spectral and spectral-element methods
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Spectral and spectral-element methods lecture notes in high performance computational physics

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


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

Book details:

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
Pagination1 v.
ID Numbers
Open LibraryOL15538727M

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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.