Isogeometric spectral approximation for elliptic differential operators
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© 2018 Elsevier B.V. We study the spectral approximation of a second-order elliptic differential eigenvalue problem that arises from structural vibration problems using isogeometric analysis. In this paper, we generalize recent work in this direction. We present optimally-blended quadrature rules for the isogeometric spectral approximation of a diffusion-reaction operator with both Dirichlet and Neumann boundary conditions. The blended rules improve the accuracy of the isogeometric approximation. In particular, the optimal blending rules minimize the dispersion error and lead to two extra orders of super-convergence in the eigenvalue error. Various numerical examples (including the Schrödinger operator for quantum mechanics) in one and three spatial dimensions demonstrate the performance of the blended rules.
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Generalization of the Pythagorean Eigenvalue Error Theorem and Its Application to Isogeometric AnalysisBarton, M.; Calo, Victor; Deng, Quanling; Puzyrev, Vladimir (2018)© 2018, Springer Nature Switzerland AG. This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric ...
Deng, Quanling; Calo, Victor (2018)We introduce the dispersion-minimized mass for isogeometric analysis to approximate the structural vibration, which we model as a second-order differential eigenvalue problem. The dispersion-minimized mass reduces the ...
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