摘要
用奇值分解和POD(proper orthogonal decomposition)基研究了一维变系数抛物问题基于POD基的有限差分格式,先用有限差分格式计算出瞬时解构成的数据集合,再用奇值分解和特征正交分解方法找出最优正交基重构这些数据集合,结合Galerkin投影方法导出了具有较高精度的低维模型,并给出了POD格式解与有限差分格式解的误差估计,数值例子表明POD格式解和有限差分格式解的误差与理论分析结果是一致的,从而验证了POD方法的有效性.
In this paper, singular value decomposition and proper orthogonal decomposition methods are used to study a finite difference scheme, based on POD for one dimension parabolic problems. The ensemble of date made up of transient solution is obtained by using finite difference scheme. The optimal othogonal bases are used to reconstruct the elements of the ensemble with POD and SVD. Combination of the above approach with a Galerkin projection procedure yields a new optimizing FDS model of lower dime-ntions and high accuracy for one dimension parabolic problems. An error estimate of the new reduced oder optimizing FDS model is then derived. Numerical example is presented to illustrate that the error between the POD approximate solution and full FDS solution is consistent with previously obtained theoretical results, thus validating the feasibility and efficiency of POD method.
出处
《贵州师范大学学报（自然科学版）》
CAS
2010年第2期88-92,共5页
Journal of Guizhou Normal University：Natural Sciences
关键词
POD基
奇值分解
差分格式
误差估计
抛物方程
POD bases
singular value decompsition
difference scheme
error estimate
quation
