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. Fractional derivatives in time and spatial coordinates are approximated using the Riemann-Liouville and Grunwald-Letnikov formulas, respectively. For parallel processing of subdomains, the formulation of local problems is organized, the formulation of local boundary and initial conditions within each subdomain is streamlined to ensure proper synchronization of the parallel algorithm, solution is updated in each subdomain, and information is transferred between subdomains to check the convergence of the method. Experimental results show that the proposed parallel algorithm has good scalability.
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