Saddle-point principles and numerical integration methods for second-order hyperbolic equations Original Research Article

This work describes a family of functionals whose stationarity – often saddle-point condition – leads to well-known so-called “variational” formulations for structural dynamics (such as the weak Hamilton/Ritz formulation and the continuous/discontinuous Galerkin formulation) and, in turn, to methods for the numerical integration of the equations of motion. It is shown that all the time integration methods based on “variational” formulations do descend from such functionals. Moreover, starting from the described family of functionals it is possible to construct new families of time integration methods, which might exhibit computational advantages over the corresponding ones derived from “variational” formulations only.