A Direct Domain Decomposition Method for Parabolic Equations and Its Application

To study the direct domain decomposition method for partial differential equations of parabilic type, the difference scheme was used to approximate the solution of the partial diferential equation. A direct domain decomposition method was presented for the parabolic partial differential equations on nonoverlapping domains. In the interior of each nonoverlapping sub domain, the values of the knots were obtained by implicit scheme while those of the interface knots by explicit difference. The information of the last time step was used to calculate the values of knots of present time step. The direct domain decomposition method given in this paper is effective for the parabolic equation.