抛物型方程的区域分解直接方法及其应用

A Direct Domain Decomposition Method for Parabolic Equations and Its Application

采用差分法近似求解偏微分方程 .研究抛物型偏微分方程的直接区域分解算法 .给出了非重叠区域上的抛物方程的区域分解直接方法 .在非重叠的子区域内部采用隐式差分格式近似微分方程 ,在子区域的交界面上 ,使用显式差分格式 ,利用上一时间层的信息求当前时间层上各节点的值 .

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.