Controlling the Critical Time Step with the Bi-Penalty Method

Abstract eng:
Penalty functions are a popular tool to add constraints to a system of equations, such as for instance Dirichlet boundary conditions or setting a relation between different degrees of freedom. Although implementation of the penalty method is simple, the commonly used stiffnesstype penalties have a drawback in dynamics in that they increase the speed of sound locally. Thus, in conditionally stable time integration schemes the critical time step is lowered (often by orders of magnitude) if stiffness penalties are used. As an alternative, one may use inertia penalties that lower the speed of sound and therefore increase the critical time step, but in this paper we suggest the simultaneous use of stiffness and inertia penalties, which is called the bipenalty method. In the bi-penalty method the relative magnitudes of stiffness penalty and inertia penalty can be tuned so that the net effect on the critical time step is neutral, thereby removing a major disadvantage of stiffness-type penalty methods.

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