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**Crystal Growth Modeling**

For some materials crystal growth processes such as Bridgman and Czochralski processes
produce crystalline materials with a large number of defects such as dislocations
and twining. Since some of these processes operate under very high pressures and
temperatures, modeling becomes an important tool to understand and control them.
In realistic situations buoyancy effects become important and cause strong convections
in the melt flow. Furthermore, they are characterized by large Grashof numbers
causing boundary layers and unstable flows. Further, since the melt flow
and the crystal quality depend on the temperature distribution, modeling accurately
the energy transfer including radiation becomes very important.
Modeling and solving the radiation-conduction-convection problem is a very challenging
and require large memory and computing power resources. New and innovative techniques are needed to solve these Three dimensional problems and control crystal growth system.
Again large Grashof numbers lead to three-dimensional flow unsteady problems which
boundary layers coupled with convection-conduction and radiant energy equation.
Obtaining numerical solutions to these problems requires the use of adaptive and
parallel algorithms. We use parallel and distributed algorithms based on domain
decomposition with dynamic load balancing.