应用数学2018，Vol.31Issue(2)：305-314,10.
基于SVD的本征正交分解算法在偏微分方程中的降阶数值模式研究
The Study About Reduced Numerical Model of Proper Orthogonal Decomposition Used in Partial Differential Equation Based on SVD
摘要
Abstract
Foundations of singular value decomposition theory(SVD)about three kinds of matrixes:the common matrix, matrix anomaly and the standard normalized matrix were discussed respectively. The SVD process of arbitrary matrix was deduced. Based on the SVD of arbitrary matrix two proper orthogonal decomposition (POD) algorithms were given. The POD algorithm combined with Galerkin projection the higher dimensional or infinite dimensional solution of partial differential equation can be projected into the complete space which was constituted by POD modes. The low dimensional solution will be obtained and the low dimensional solution will be compared with the solution of partial differential equation. The stability and accuracy of the POD algorithm also will be compared between the solution of partial differential equation and the low dimensional solutions obtained by different POD modes. At last some numerical examples were given to show the pros and cons and its applicability of two kinds of POD algorithms.关键词
奇异值分解/本征正交分解/偏微分方程/降阶数值模式Key words
Singular value decomposition/Proper orthogonal decomposition/Partial differential equation/Reduced numerical model分类
数理科学引用本文复制引用
曹艳华,张静静..基于SVD的本征正交分解算法在偏微分方程中的降阶数值模式研究[J].应用数学,2018,31(2):305-314,10.基金项目
国家自然科学基金(11461026),国家自然科学基金(11661036) （11461026）
