扩散方程区域分解的多步算法  

Domain Decomposition Algorithm with Multi-step Evaluation for Diffusion Equation

作　　者：盛志明[1] 崔霞[2] 刘兴平[2] 

机构地区：[1]中国工程物理研究院研究生部,北京100088 [2]北京应用物理与计算数学研究所计算物理重点实验室,北京100088

出　　处：《计算物理》2011年第6期825-830,共6页Chinese Journal of Computational Physics

基　　金：国家自然科学基金(60973151;11071024;10871029);国防基础科研项目(B1520110011);中国工程物理研究院科学技术基金(2010A0202010);计算物理实验室基金资助项目

摘　　要：利用分数步法进行内边界值的多步计算,改进二维扩散方程的区域分解算法,形成新的并行算法,放宽稳定性条件.其中采用分数步空间大步长离散格式计算内边界点值.算法精度与隐格式相当.与改进前相比,稳定性条件放宽了q倍(q为两个相邻时间步之间执行分数步内边界值计算的次数).利用离散极值原理,严格证明了算法的收敛性.在并行机上进行数值试验,验证理论分析的结果,表明算法具有更宽松的稳定性、好的精度和并行可扩展性.Domain decomposition parallel algorithms for one-and two-dimensional diffusion equations are studied by using multi-step evaluation revisions for interface points with fractional temporal index.Stability conditions are loose.In the algorithm,schemes with fractional step and large spacing discretization are used to evaluate interface points.The algorithms have same accuracy as full implicit method,while their stability bounds are released by q,the number of fractional step evaluations on interfaces between two neighboring temporal steps,times compared with existing algorithms.Convergence is proven rigorously with discrete maximum principle.Numerical experiments on parallel computers confirm theoretical conclusions.They demonstrate looser stability conditions,good accuracy and parallel expansibility of the algorithms.

关 键 词：扩散方程 区域分解 并行计算 多步法 

分 类 号：O241.82[理学—计算数学] O246[理学—数学]