When the final interface sha pe and temperature distribution are obtained, the data on grid field and temperature are transferred to FEM module to calculate the thermal stress. The finite element scheme uses a displacement based formulation. The stiffness matrix is calculated for every element and then assembled into the global stiffness matrix. For numerical integration, the Gaussian quadrature is used. The element numbering stratergy has been carefully selected to reduce the semi-bandwidth.
Penalty method is used to set the external load at a specific node.
A direct Gaussian elimination method is used to solve the equations. In order to save space for both assembly and so lution, a bounded solver is adopted which proves to be sufficient for the present problem. Once the dispacements are obtained, stresses can be recovered at Gaussian points. Figure 3 and Figure 4 present snapshots of simulation results, at different stages of the growth, when a 40mm dia crystal is being grown. Figure 5 presents the stress along the interface at different heights of the crystal, during the growth process.