A Feed-Forward Neural Network for Solving Stokes Problem

被引：3
作者：
Baymani, M. [1 ]
Effati, S. [2 ]
Kerayechian, A. [2 ]
机构：
[1] Quchan Inst Engn & Technol, Dept Math, Quchan, Iran
[2] Ferdowsi Univ Mashhad, Dept Appl Math, Mashhad, Iran
来源：
ACTA APPLICANDAE MATHEMATICAE | 2011年 / 116卷 / 01期
关键词：
Artificial neural networks; Stokes problem; Poisson equation; Partial differential equations; FINITE-ELEMENT METHODS; H(DIV) ELEMENTS; EQUATIONS;
D O I：
10.1007/s10440-011-9627-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The current research attempts to offer a novel method for solving the Stokes problem based on the use of feed-forward neural networks. We transform the mixed Stokes problem into three independent Poisson problems which by solving them the solution of the Stokes problem is obtained. The results obtained by this method, has been compared with the existing numerical method and with the exact solution of the problem. It can be observed that the current new approximation has higher accuracy. The number of model parameters required is less than conventional methods. The proposed new method is illustrated by two examples.
引用
收藏
页码：55 / 64
页数：10
相关论文
共 22 条
[1]  
Aman M., 2004, INT MATH J, V5, P9
[2]  
[Anonymous], 2015, Linear and Nonlinear Programming
[3]  
Cockburn B, 2005, MATH COMPUT, V74, P1067, DOI 10.1090/S0025-5718-04-01718-1
[4]   Local discontinuous Galerkin methods for the Stokes system [J].
Cockburn, B ;
Kanschat, G ;
Schotzau, D ;
Schwab, C .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 40 (01) :319-343
[5]  
Davidon W., 1959, ANL-5990 Rev
[6]  
DEBAR H, 1992, P IEEE COMP SOC S RE
[7]  
Eymard R., 2005, INT J FINITE ELECT, V2
[8]   A RAPIDLY CONVERGENT DESCENT METHOD FOR MINIMIZATION [J].
FLETCHER, R ;
POWELL, MJD .
COMPUTER JOURNAL, 1963, 6 (02) :163-&
[9]   A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems [J].
Girault, V ;
Rivière, B ;
Wheeler, MF .
MATHEMATICS OF COMPUTATION, 2005, 74 (249) :53-84
[10]  
Girault V., 2012, Finite Element Methods for NavierStokes Equations: Theory and Algorithms
123