Conservative domain decomposition procedure with unconditional stability and second-order accuracy

A new derivation of the conservative domain decomposition procedure for solving the parabolic equation is presented. In this procedure, fluxes at subdomain interfaces are calculated from the solution at the previous time level, then these fluxes serve as Neumann boundary data for implicit, block-centered discretization in the subdomain. The unconditional stability and the second-order accuracy of solution values as well as fluxes are proved. Numerical results examining the stability, accuracy, and parallelism of the procedure are also presented.