EigenValue Stabilization in Explicit Immersed Simulations
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The small cut element problem is common to all immersed boundary methods and leads to stability as well as conditioning problems in static analyses. Considering explicit dynamics, restrictions on the critical time step size are also observed. To be precise, the time step size does not only scale inversely with the polynomial degree of the shape functions, but also with the volume fraction of cut elements. Therefore, measures need to be taken to increase the time step size. Possible ideas range from selective mass scaling of poorly cut elements to the application of IMEX (implicit-explicit) or asynchronous time integration schemes. In this contribution, we, however, want to focus our investigations on the recently introduced eigenvalue stabilization (EVS) technique. Initially applied to crack propagation problems [1] in the context of XFEM (extended finite element method), its potential for immersed methods was soon realized [2], where non-linear static problems were analyzed. An extension to transient simulations, targeting especially explicit time integration algorithms, was achieved in Ref. [3]. Here, a noteworthy increase in the critical time step size was observed along with a drastic reduction in the condition number of the system matrices.
