高维抛物方程迎风区域分裂差分方法

Domain Decomposition Upwind Difference Schemes for Multidimensional Parobolic Problems

结合迎风方法和区域分裂思想,采用一阶迎风、二阶修正迎风法逼近高维抛物方程的对流项.内边界处和子区域分别对应区域分裂显隐格式;并运用极值原理和嵌入定理给出了收敛性分析,最后给出数值试验,说明其实际意义.

Combining the domain decomposition with upwind difference method, the authors present the convection part of multidimensional parabolic problems is discretized by the 1- order upwind method and the modified 2-order upwind method. The proposed schemes rely on implicit procedures in subdomains and explicit calculation on the inter-domain boundaries. With certain stability conditions, convergence analysis is presented by the maximum principle and embedding theorem. Finally, numerical examples illustrating the value, accuracy and parallelism are shown.