To effectively simulate the time evolution of the dislocation density during the crystal growth process under high stress by the Alexander-Haasen model, a fully implicit and fully coupled implementation of the Alexander-Haasen model has been proposed. Numerical tests on low-stress multicrystalline silicon grown in a small furnace and high-stress seed-cast monocrystalline silicon grown in an industrial-scale furnace have been done. Results indicate that the proposed algorithm is highly efficient, strongly stable and applicable to any stress level. This algorithm provides an effective tool to optimize the crystal growth process and reduce dislocation density in industrial-scale furnaces. (C) 2013 Elsevier B.V. All rights reserved.