
Outlier removal for isogeometric spectral approximation with the optimallyblended quadratures
It is wellknown that outliers appear in the highfrequency region in th...
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The Infinity Laplacian eigenvalue problem: reformulation and a numerical scheme
In this work we present an alternative formulation of the higher eigenva...
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Direct guaranteed lower eigenvalue bounds with optimal a priori convergence rates for the biLaplacian
An extrastabilised Morley finite element method (FEM) directly computes...
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Approximation of the zeroindex transmission eigenvalues with a conductive boundary and parameter estimation
In this paper, we present a SpectralGalerkin Method to approximate the ...
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Novel design and analysis of generalized FE methods based on locally optimal spectral approximations
In this paper, the generalized finite element method (GFEM) for solving ...
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Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations
We show that isogeometric Galerkin discretizations of eigenvalue problem...
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Analysis of radial complex scaling methods: scalar resonance problems
We consider radial complex scaling/perfectly matched layer methods for s...
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A boundary penalization technique to remove outliers from isogeometric analysis on tensorproduct meshes
We introduce a boundary penalization technique to improve the spectral approximation of isogeometric analysis (IGA). The technique removes the outliers appearing in the highfrequency region of the approximate spectrum when using the C^p1, pth (p≥3) order isogeometric elements. We focus on the classical Laplacian (Dirichlet) eigenvalue problem in 1D to illustrate the idea and then use the tensorproduct structure to generate the stiffness and mass matrices for multiple dimensional problems. To remove the outliers, we penalize the product of the higherorder derivatives from both the solution and test spaces at the domain boundary. Intuitively, we construct a better approximation by weakly imposing features of the exact solution. Effectively, we add terms to the variational formulation at the boundaries with minimal extra computational cost. We then generalize the idea to remove the outliers for the isogeometric analysis to the Neumann eigenvalue problem (for p≥2). The boundary penalization does not change the test and solution spaces. In the limiting case when the penalty goes to infinity, we perform the dispersion analysis of C^2 cubic elements for Dirichlet eigenvalue problem and C^1 quadratic elements for Neumann eigenvalue problem. We obtain the analytical eigenpairs for the resulting matrix eigenvalue problems. Numerical experiments show optimal convergence rates for the eigenvalues and eigenfunctions of the discrete operator.
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