Displaying similar documents to “A Legendre spectral collocation method for the biharmonic Dirichlet problem”

A Legendre Spectral Collocation Method for the Biharmonic Dirichlet Problem

Bernard Bialecki, Andreas Karageorghis (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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A Legendre spectral collocation method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which are linear combinations of Legendre polynomials. A Schur complement approach is used to reduce the resulting linear system to one involving the approximation of the Laplacian of the solution on the two vertical sides of the square. The Schur complement system is...

Prediction of natural frequencies of laminated curved panels using refined 2-D theories in the spectral collocation method

Amir Hossein Mohazzab, Lorenzo Dozio (2015)

Curved and Layered Structures

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This paper presents a versatile and efficientmodeling and solution framework for free vibration analysis of composite laminated cylindrical and spherical panels modeled according to two-dimensional equivalent singlelayer and layerwise theories of variable order.Aunified formulation of the equations of motion is adopted which can be used for both thin and thick structures. The discretization procedure is based on the spectral collocation method and is presented in a compact matrix form...

Finite-difference preconditioners for superconsistent pseudospectral approximations

Lorella Fatone, Daniele Funaro, Valentina Scannavini (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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The superconsistent collocation method, which is based on a collocation grid different from the one used to represent the solution, has proven to be very accurate in the resolution of various functional equations. Excellent results can be also obtained for what concerns preconditioning. Some analysis and numerous experiments, regarding the use of finite-differences preconditioners, for matrices arising from pseudospectral approximations of advection-diffusion boundary value problems,...