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

作　　者：李长峰[1] 袁益让[2] 

机构地区：[1]山东大学经济学院,济南250100 [2]山东大学数学研究所,济南250100

出　　处：《数学物理学报（A辑）》2007年第5期879-889,共11页Acta Mathematica Scientia

基　　金：国家重点基础研究专项经费(G1999032803);国家自然科学基金(10372052;10271066);教育部博士点基金(20030422047)资助

摘　　要：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.

关 键 词：区域分裂 并行计算 迎风差分 误差估计 

分 类 号：O241.82[理学—计算数学]