Time integration and the Trefftz Method Part II - Second-order and hyperbolic problems - Freitas, João A. Teixeira de (Computer Assisted Methods in Engineering and Science; Vol 10 No 4 (2003), 2023)
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 single- and double-field formulations are presented and the associated Trefftz formulations are established.