  We describe and evaluate a numerical solution strategy for simulating surface
acoustic waves through semiconductor devices with complex geometries. This
multi-physics problem is of particular relevance to the design of quantum
electronic devices. The mathematical model consists of two coupled partial
differential equations for the elastic wave propagation and the electric field,
respectively, in anisotropic piezoelectric media. These equations are
discretized by the finite element method in space and by a finite difference
method in time. The latter method yields a convenient numerical decoupling of
the governing equations. We describe how a computer implementation can utilize
the decoupling and via object-oriented programming techniques reuse independent
codes for the Poisson equation and the linear time-dependent elasticity
equation. First we apply the simulator to a simplified model problem for
verifying the implementation, and thereafter we show that the methodology is
capable of simulating a real-world case from nanotechnology, involving surface
acoustic waves in a geometrically non-trivial device made of Gallium Arsenide.
