The new mass-conserving S-DDM scheme for two-dimensional parabolic equations with variable coefficients

In the article, a new and efficient mass-conserving operator splitting domain decomposition method (S-DDM) is proposed and analyzed for solving two dimensional variable coefficient parabolic equations with reaction term. The domain is divided into multiple non-overlapping block-divided subdomains. On each block-divided subdomain, the interface fluxes are first computed explicitly by local multi-point weighted schemes and the solutions in the interior of subdomain are computed by the one-directional operator splitting implicit schemes at each time step. The scheme is proved to satisfy mass conservation over the whole domain of domain decomposition. By combining with some auxiliary lemmas and applying the energy method, we analyze theoretically the stability of our scheme and prove it to have second order accuracy in space step in the L2 norm. Numerical experiments are performed to illustrate its accuracy, conservation, stability, efficiency and parallelism. Our scheme not only keeps the excellent advantages of the non-overlapping domain decomposition and the operator splitting technique, but also preserves the global mass.