  Accelerated algorithms for simulating the morphological evolution of strained
heteroeptiaxy based on a ball and spring lattice model in three dimensions are
explained. We derive exact Green's function formalisms for boundary values in
the associated lattice elasticity problems. The computational efficiency is
further enhanced by using a superparticle surface coarsening approximation.
Atomic hoppings simulating surface diffusion are sampled using a multi-step
acceptance-rejection algorithm. It utilizes quick estimates of the atomic
elastic energies from extensively tabulated values modulated by the local
strain. A parameter controls the compromise between accuracy and efficiency of
the acceptance-rejection algorithm.
