Time integration and the Trefftz Method, Part II – Second-order and hyperbolic problems

The finite element method is applied in the time domain to establish formulations for the integration of second-order and hyperbolic (dynamic) problems. Modal decomposition in the space domain is used to recover the well-established method for uncoupling the equations of motion, which is extended to include general time approximation bases. The limitations of this approach in the implementation of large-scale, non-linear problems while preserving the uncoupling of the equations of motion are overcome by using the alternative concept of modal decomposition in the time domain. Both singleand double-field formulations are presented and the associated Trefftz formulations are established.