Hybrid numerical scheme for time-evolving wave fields

Many problems in geophysics, acoustics, elasticity theory, cancer treatment, food process control and electrodynamics involve study of wave field synthesis (WFS) in some form or another. In the present work, modelling of wave propagation phenomena is studied as a static problem, using finite element method and treating time as an additional spatial dimension. In particular, WFS problems are analysed using discrete methods. It is shown that a fully finite element-based scheme is very natural and effective method for the solution of such problems. Distributed WFS in the context of two-dimensional problems is outlined and incorporation of any geometric or material non-linearities is shown to be straightforward. This has significant implications for problems in geophysics or biological media, where material inhomogeneities are quite prevalent. Numerical results are presented for several problems referring to media with material inhomogeneities and predefined absorption profiles. The method can be extended to three-dimensional problems involving anisotropic media properties in a relatively straightforward manner.