缩减基有限元方法快速求解参数化偏微分方程  

Reduced Basis Finite Element Method for Fast Solution of Parameterized Partial Differential Equations

作　　者：陈恭 王一正 王烨 张纯禹 CHEN Gong;WANG Yizheng;WANG Ye;ZHANG Chunyu(Sino-French Institute of Nuclear Engineering and Technology,Sun Yat-Sen Univeristy,Zhuhai Guangdong,519082,China)

机构地区：[1]中山大学中法核工程与技术学院

出　　处：《计算物理》2018年第5期515-524,共10页Chinese Journal of Computational Physics

基　　金：NSFC-广东联合基金超级计算科学应用专项(20144500031650003)资助项目

摘　　要：针对可用参数化微分方程表示的问题,缩减基有限元方法利用典型参数的高精度解构造基函数,可大幅度降低待求问题的自由度.以固体热传导和中子扩散的快速求解为例,展示该方法的优良特性.结果表明：在线阶段的求解效率可以实现两到三个数量级的提升.基于高保真模拟的缩减基模型可使高性能计算有效地应用于工程优化设计、应急指挥及复杂问题的反分析等.For problems that can be described by parameterized partial differential equations,reduced basis finite element constructs basis functions on top of typical high-fidelity solutions and thus greatly reduces number of unknowns. Principles of the method is introduced and favorable features are demonstrated through heat conduction problem and neutron diffusion problem. It shows speedup of three orders of magnitude during online stage.

关 键 词：缩减基 有限元 后验误差 热传导 中子扩散 

分 类 号：O242.21[理学—计算数学]