A reduced-order extrapolated natural boundary element method based on POD for the parabolic equation in the 2D unbounded domain

2019 ◽  
Vol 38 (3) ◽  
Author(s):  
Fei Teng ◽  
Zhen Dong Luo ◽  
Jing Yang
Keyword(s):  
Parabolic Equation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Unbounded Domain ◽  
Natural Boundary ◽  
Reduced Order ◽  
Natural Boundary Element Method ◽  
Element Method

WAVELET NATURAL BOUNDARY ELEMENT METHOD FOR THE NEUMANN EXTERIOR PROBLEM OF STOKES EQUATIONS

2006 ◽  
Vol 04 (01) ◽  
pp. 23-39 ◽  
Author(s):  
WEN-SHENG CHEN ◽  
XINGE YOU ◽  
BIN FANG ◽  
YUANYAN TANG ◽  
JIAN HUANG
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Stiffness Matrix ◽  
Stokes Equations ◽  
Exterior Problem ◽  
Natural Boundary ◽  
Node Number ◽  
Element Approach ◽  
Natural Boundary Element Method ◽  
Element Method

Natural boundary element approach is a promising method to solve boundary value problems of partial differential equations. This paper addresses the Neumann exterior problem of Stokes equations using the wavelet natural boundary element method. The Stokes exterior problem is reduced into an equivalent Hadamard-singular Natural Integral Equation (NIE). By virtue of the wavelet-Galerkin algorithm, the simple and accurate computational formulae of stiffness matrix are obtained. The 2J+3 × 2J+3 stiffness matrix is sparse and determined only by its 2J + 3J + 1 entries. It greatly decreases the computational complexity. Also, the condition number of stiffness matrix is [Formula: see text], where N is the discrete node number. This indicates that the proposed algorithm is more stable than that of classical finite element method. The error estimates are established for the wavelet-Galerkin approximate solution. Several numerical examples are given to evaluate the performance of our method with encouraging results.

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