Modeling of industrial bulk crystal growth-state of the art and challenges

Numerical modeling has become an indispensable and acknowledged tool for developing and optimizing crystal growth processes and equipment. Although the state of the art allows efficient use of simulation in both academic and industrial crystal growth, modeling of crystal growth is on its way to its own next generation with extended application fields, more powerful hardware, and increasingly sophisticated numerical methods, especially from the field of soft-computing. One very promising approach is the combination of genetic algorithms with conventional thermal modeling. The great benefit of numerical modeling is demonstrated by some current examples from different fields of bulk crystal growth, treated either by classical global modeling or by additional use of genetic algorithms.