Mass lumping and stabilization for immersogeometric analysis

TL;DR

This paper investigates the effects of mass lumping in immersogeometric analysis, revealing accuracy issues in low frequencies and proposing a polynomial extension stabilization method to improve solution fidelity.

Contribution

It identifies the accuracy degradation caused by mass lumping in smooth isogeometric discretizations and introduces a novel stabilization technique to mitigate this problem.

Findings

Mass lumping can cause spurious oscillations in low-frequency modes.

The proposed polynomial extension stabilization restores accuracy.

Mass lumping's impact on low frequencies is significant and previously overlooked.

Abstract

Trimmed (multi-patch) geometries are the state-of-the-art technology in computer-aided design for industrial applications such as automobile crashworthiness. In this context, fast solution techniques extensively rely on explicit time integration schemes in conjunction with mass lumping techniques that substitute the consistent mass with a (usually diagonal) approximation. For smooth isogeometric discretizations, Leidinger [1] first showed that mass lumping removed the dependency of the critical time-step on the size of trimmed elements. This finding has attracted considerable attention but has unfortunately overshadowed another more subtle effect: mass lumping may disastrously impact the accuracy of low frequencies and modes, potentially inducing spurious oscillations in the solution. In this article, we provide compelling evidence for this phenomenon and later propose a stabilization technique based on polynomial extensions that restores a level of accuracy comparable to boundary-fitted discretizations.