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Explicit time-marching schemes are popular for solving time-dependent partialdifferential equations; one of the biggest challenges these methods suffer isincreasing the critical time-marching step size that guarantees numericalstability. In general, there are two ways to increase the critical step size.One is to reduce the stiffness of the spatially discretized system, while theother is to design time-marching schemes with larger stability regions. In thispaper, we focus on the recently proposed explicit generalized-$\alpha$ methodfor second-order hyperbolic equations and increase the critical step size byreducing the stiffness of the isogeometric-discretized system. In particular,we apply boundary penalization to lessen the system's stiffness. For $p$-thorder $C^{p-1}$ isogeometric elements, we show numerically that the criticalstep size increases by a factor of $\sqrt{\frac{p^2-3p+6}{4}}$, which indicatesthe advantages of using the proposed method, especially for high-orderelements. Various examples in one, two, and three dimensions validate theperformance of the proposed technique.

A boundary-penalized isogeometric analysis for second-order hyperbolic equations