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

TL;DR

This paper introduces a variational method using perturbed eigenvalue analysis to eliminate outlier frequencies in isogeometric multipatch discretizations, enhancing spectral properties and enabling larger time steps in explicit dynamics.

Contribution

It presents a novel variational approach and iterative procedure to remove outlier frequencies without compromising overall spectral accuracy.

Findings

Outlier frequencies are effectively eliminated.

Larger critical time-step sizes are achieved in explicit dynamics.

The approach's effectiveness is independent of spline polynomial degree.

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.