Impurities and dislocations in silicon crystals can cause significant deterioration in the conversion efficiency of solar cells. For increasing solar cell efficiency, reduction of impurities and dislocations is necessary. Numerical simulation is a powerful tool for improving the quality of silicon crystal for solar cells. A set of numerical analysis system that includes all processes involved in crystal growth has been developed for studying the carbon and oxygen transport in global furnace, and a three-dimensional Alexander-Haasen model was developed for studying the dislocation multiplication. The simulation helped to reduce carbon and oxygen impurities by designing a simple crucible cover and to decrease the dislocation multiplication and residual stress by using a slow cooling process. Further quality improvements can be achieved using these solvers to optimize furnace structure and operating conditions at a low cost.