Domain decomposition

Based on the Schwarz method, a parallel algorithm has been developed for partitioning a two-dimensional discretization domain into overlapping subdomains to solve a system of partial differential equations of fractional order that describes heat and mass transfer processes in anisotropic media with a fractal structure. Using the finite difference method, explicit difference schemes for temperature and moisture equations in subdomains are derived.

The paper discusses versatile constraint equations used for providing compatibility between the solutions obtained for separate sub-domains of electromagnetic field which are analyzed simultaneously. The mathematical model of the task has been developed using invariant approximation technique for finite-difference method. Different techniques for domain decomposition are considered. The discussed constraint equations and domain decomposition techniques have been applied to solving a test problem, and namely the problem of magnetic skin-effect.