A variational approach based on perturbed eigenvalue analysis for improving spectral properties of isogeometric multipatch discretizations

Abstract

A key advantage of isogeometric discretizations is their accurate and well-behaved eigenfrequencies and eigenmodes. For degree two and higher, however, optical branches of spurious outlier frequencies and modes may appear due to boundaries or reduced continuity at patch interfaces. In this paper, we introduce a variational approach based on perturbed eigenvalue analysis that eliminates outlier frequencies without negatively affecting the accuracy in the remainder of the spectrum and modes. We then propose a pragmatic iterative procedure that estimates the perturbation parameters in such a way that the outlier frequencies are effectively reduced. We demonstrate that our approach allows for a much larger critical time-step size in explicit dynamics calculations. In addition, we show that the critical time-step size obtained with the proposed approach does not depend on the polynomial degree of spline basis functions.

References in corpus (3)

• A boundary penalization technique to remove outliers from isogeometric analysis on tensor-product meshes
• Outlier removal for isogeometric spectral approximation with the optimally-blended quadratures
• Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations

Cited by in corpus (5)

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• A comparison of smooth basis constructions for isogeometric analysis
• Variationally consistent mass scaling for explicit time-integration schemes of lower- and higher-order finite element methods
• Nonlinear dynamic analysis of shear- and torsion-free rods using isogeometric discretization and outlier removal