Variational Methods for Time-Dependent Wave Propagation Problems

There is an important need for numerical methods for time dependent wave propagation problems and their many applications, for example in acoustics, electromagnetics and geophysics. Although very old, finite difference time domain methods (FDTD methods in the electromagnetics literature) remain very popular and are widely used in wave propagation simulations, and more generally for the resolution of linear hyperbolic systems, among which Maxwell's system is a typical example. These methods allow us to get discrete equations whose unknowns are generally field values at the points of a regular mesh with spatial step h and time step Δt.