Spectral-accuracy effects of row-sum mass lumping in strongly nonlinear dynamics

Determine whether mass-lumping-related spectral inaccuracies are significant in strongly nonlinear simulations, particularly when lower-spectrum spurious modes may influence transient response.

Background

The paper distinguishes between controlling the upper spectral limit, which governs the critical explicit time step, and controlling the accuracy of the lower discrete spectrum. Prior studies indicate that row-sum mass lumping can produce spurious low-frequency modes in trimmed or immersed spline discretizations, but their practical impact depends on the application and nonlinear regime.

The authors report that the influence of mass-lumping-related inaccuracies is not established for strongly nonlinear simulations and explicitly limit the present work to the upper spectral bound. Thus, the unresolved issue concerns whether such lower-spectrum inaccuracies materially affect strongly nonlinear dynamic responses.

References

These findings indicate a strong dependence on the considered application and nonlinear regime, but do not establish that mass-lumping-related spectral inaccuracies are generally negligible in strongly nonlinear simulations. Their relevance in such applications therefore remains an open question.

— Boundary-Level-Constrained Refinement for Suppressing Trimming-Induced High-Frequency Outliers in Explicit Isogeometric Analysis  (2609.10161 - Hollweck et al., 9 Sep 2026) in Section 1, Introduction

Although this may mitigate spectral outliers, it alters the total mass and inertia of the system. Determining suitable scaling factors and assessing their impact on highly nonlinear simulations, including contact, plasticity, and damage, remains an open problem.

— Boundary-Level-Constrained Refinement for Suppressing Trimming-Induced High-Frequency Outliers in Explicit Isogeometric Analysis  (2609.10161 - Hollweck et al., 9 Sep 2026) in Section 5, Conclusion and Outlook