Outlier removal for isogeometric spectral approximation with the optimally-blended quadratures

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.