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The application of immersed boundary methods in static analyses is oftenimpeded by poorly cut elements (small cut elements problem), leading toill-conditioned linear systems of equations and stability problems. While theseconcerns may not be paramount in explicit dynamics, a substantial reduction inthe critical time step size based on the smallest volume fraction $\chi$ of acut element is observed. This reduction can be so drastic that it rendersexplicit time integration schemes impractical. To tackle this challenge, wepropose the use of a dedicated eigenvalue stabilization (EVS) technique.  The EVS-technique serves a dual purpose. Beyond merely improving thecondition number of system matrices, it plays a pivotal role in extending thecritical time increment, effectively broadening the stability region inexplicit dynamics. As a result, our approach enables robust and efficientanalyses of high-frequency transient problems using immersed boundary methods.A key advantage of the stabilization method lies in the fact that onlyelement-level operations are required.  This is accomplished by computing all eigenvalues of the element matrices andsubsequently introducing a stabilization term that mitigates the adverseeffects of cutting. Notably, the stabilization of the mass matrix$\mathbf{M}_\mathrm{c}$ of cut elements -- especially for high polynomialorders $p$ of the shape functions -- leads to a significant raise in thecritical time step size $\Delta t_\mathrm{cr}$.  To demonstrate the efficacy of our technique, we present two specificallyselected dynamic benchmark examples related to wave propagation analysis, wherean explicit time integration scheme must be employed to leverage the increasein the critical time step size.

An EigenValue Stabilization Technique for Immersed Boundary Finite Element Methods in Explicit Dynamics