Higher order variational space-time approximation of wave propagation

The accurate and reliable numerical approximation of wave propagation is of fundamental importance to the simulation of acoustic, electromagnetic and elastic phenomena. In mechanical engineering, advanced composites such as carbon fibre reinforced polymer have become one of the most promising materials to build light-weight structures for several fields of application, for instance in aerospace and automotive fields, in wind energy, as well as in sailboats, and in modern bicycles, motorcycles and sport cars. These composits are able to combine the high strength and rigidity of the reinforced fiber with excellent properties of synthetic resins in best possible way. Material inspection by piezoelectric induced ultrasonic waves is a relatively new and an intelligent technique to monitor the health of carbon fibre reinforced polymer, for damage detection (delamination, matrix cracks, fibre breaks) and non-destructive evaluation. For the design of structural health monitoring systems it is strictly necessary to understand phenomenologically and quantitatively wave propagation in carbon fibre reinforced polymer and the influence of the geometrical and mechanical properties of the system structure. Numerical simulation is a promising way to achieve this goal. Therefore, the ability to solve numerically the wave equation in three space dimensions is particularly important from the point of view of physical realism. However, this is still a challenging task and an active area of research.