  A numerical method for computation of heteroepitaxial growth in the presence
of strain is presented. The model used is based on a solid-on-solid model with
a cubic lattice. Elastic effects are incorporated using a ball and spring type
model. The growing film is evolved using Kinetic Monte Carlo (KMC) and it is
assumed that the film is in mechanical equilibrium. The strain field in the
substrate is computed by an exact solution which is efficiently evaluated using
the fast Fourier transform. The strain field in the growing film is computed
directly. The resulting coupled system is solved iteratively using the
conjugate gradient method. Finally we introduce various approximations in the
implementation of KMC to improve the computation speed. Numerical results show
that layer-by-layer growth is unstable if the misfit is large enough resulting
in the formation of three dimensional islands.
