AN EFFICIENT METHOD TO SOLVE POORLY CONDITIONED 3D ELLIPTICAL EQUATIONS FOR THE CASE OF STEPHAN MELT CRYSTALLIZATION PROBLEM
V. R Ginkin, O. M. Ginkina, S. M. Ganina, K. G. Chernov, S. V. Pupko, A. B. Kagalenko
VANT. Ser.: Mat. Mod. Fiz. Proc 2006. Вып.4. С. 45-57.
The new efficient technique called CGPIF has been developed to solve 3D finite-difference elliptical equations with symmetric poorly- conditioned matrices of coefficients. Two-level iterative technique has been proposed to solve asymmetric problems using CGPIF technique in inner iterations. The convergence rate of the proposed technique has been studied using Dirichlet and Neumann test problems for diffusion and diffusion-convection equations. The new mathematical model is proposed to solve Stephan problem in enthalpy variables along with convection heat-and-mass transfer in liquid phase. The results of experimental benchmarks of melt crystallization are given which demonstrate model adequacy.
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