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 Greens function formalisms for boundary values in the associated l
attice 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.
