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We describe an alternative approach to perform growth simulations that combines the kinetic Monte Carlo ͑KMC͒ method with elements from continuum and rate equations. Similar to the KMC method it takes the atomistic structure of the growing surface fully into account but is based on the adatom density rather than on explicit trajectories of the adatoms. As will be demonstrated, this approach decouples the fast time scale of adatom motion from the much slower time scale of changes in growth morphology. This decoupling allows a reduction of the number of simulation time steps by several orders of magnitude. Based on a comparison with the KMC calculation performance, reliability and limits of this approach are discussed.

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