### ASA 125th Meeting Ottawa 1993 May

## 2pPA2. ``Wave automation'' for wave propagation in the time domain.

**Didier Sornette
**

**
Patrick Sebbah
**

**
Christian Vanneste
**

**
**
*Lab. de Phys. de la Matiere Condensee, CNRS URA 190, Univ. de
Nice---Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 2, France
*

*
*
The new model introduced recently [Vanneste et al., Europhys. Lett. 17,
715 (1992)] for the dynamical propagation of waves in arbitrary heterogeneous
media, which is efficient for calculations on large systems (1024x1024) over
long times (several 10[sup 6] inverse band widths) will be discussed. Instead
of starting from a wave equation or a Hamiltonian that needs to be discretized
for numerical implementation, the model is defined by the set of S matrices,
one for each node, describing the interaction of the wave field with the
scatterers. The different results are shown on wave packets in random media,
which have been obtained using extensive numerical simulations on a parallel
computer and these numerical results are compared with weak localization
predictions. Finally, ``wave automaton'' is shown to be equivalent to a
discretized version of the hyperbolic time-dependent wave and Klein--Gordon
equations, when restricted to a suitable subclass of the control parameters,
and the relationships between the two formulations of the wave propagation
problem are made explicit. Compared to finite-difference versions of hyperbolic
equations, the wave automaton is shown to be much more flexible for
implementing arbitrary boundary conditions.