Additive splitting methods for elliptic-parabolic problems

Three finite-difference splitting schemes are proposed for numerical solution of the nonlinear 3D parabolic-elliptic problem. Adaptive front-tracking and time-stepping strategies are included into the algorithms. Parallelization of the algorithms is done using the domain decomposition method. The 1D decomposition of the computational domain is used in order to obtain the optimal computational load balancing among processors and to minimize the frequency of data communications. A redistribution of the computational domain among processors is done dynamically during computations.