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Outlier Removal for Isogeometric Spectral Approximation with the Optimally-Blended Quadratures

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Computational Science – ICCS 2021 (ICCS 2021)

Abstract

It is well-known that outliers appear in the high-frequency region in the approximate spectrum of isogeometric analysis of the second-order elliptic operator. Recently, the outliers have been eliminated by a boundary penalty technique. The essential idea is to impose extra conditions arising from the differential equation at the domain boundary. In this paper, we extend the idea to remove outliers in the superconvergent approximate spectrum of isogeometric analysis with optimally-blended quadrature rules. We show numerically that the eigenvalue errors are of superconvergence rate \(h^{2p+2}\) and the overall spectrum is outlier-free. The condition number and stiffness of the resulting algebraic system are reduced significantly. Various numerical examples demonstrate the performance of the proposed method.

This work and visit of Quanling Deng in Krakow was partially supported by National Science Centre, Poland grant no. 017/26/M/ST1/00281. This publication was made possible in part by the CSIRO Professorial Chair in Computational Geoscience at Curtin University and the Deep Earth Imaging Enterprise Future Science Platforms of the Commonwealth Scientific Industrial Research Organisation, CSIRO, of Australia. Additional support was provided by the European Union’s Horizon 2020 Research and Innovation Program of the Marie Sklodowska-Curie grant agreement No. 777778 and the Curtin Institute for Computation.

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Deng, Q., Calo, V.M. (2021). Outlier Removal for Isogeometric Spectral Approximation with the Optimally-Blended Quadratures. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12743. Springer, Cham. https://doi.org/10.1007/978-3-030-77964-1_25

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  • DOI: https://doi.org/10.1007/978-3-030-77964-1_25

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