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Spectral collocation methods in solid mechanics
Trnka, Ladislav ; Průša, Vít (advisor) ; Zeman, Jan (referee)
Spectral collocation methods are advertised as a powerful tool for a numerical so- lution of boundary value problems for ordinary as well as partial differential equations. The methods are based on a polynomial approximation, typically using Chebyshev poly- nomials. In one-dimensional setting, the properties of the methods are well known, and there exist several software packages implementing the methods. Our goal is to assess the applicability of spectral collocation methods in solving two-dimensional boundary value problems. We solve a classical problem in linearised two-dimensional elasticity, namely the deflection of a semi-infinite elastic medium subject to a surface load. The numerical results are compared to the analytical solution, which allows us to evaluate the performance of the given numerical method in solving boundary value problems in linearised elasticity. 1

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