Stability of an explicit multi-time step integration algorithm for linear structural dynamics equations

A proof of stability is developed for an explicit multi-time step integration method of the second order differential equations which result from a semidiscretization of the equations of structural dynamics. The proof is applicable to an algorithm that partitions the mesh into subdomains according to nodal groups which are updated with different time steps. The stability of the algorithm is demonstrated by showing that the eigenvalues of the amplification matrices lie within the unit circle and that a pseudo-energy remains constant. Bounds on the stable time steps for the nodal partitions are developed in terms of element frequencies.