Methods for dimension reduction and their application in nonlinear dynamics

被引:98
作者
Steindl, A [1 ]
Troger, H [1 ]
机构
[1] Vienna Univ Technol, Inst Mech, A-1040 Vienna, Austria
基金
奥地利科学基金会;
关键词
nonlinear dynamics; dimension reduction; Galerkin methods;
D O I
10.1016/S0020-7683(00)00157-8
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
We compare linear and nonlinear Galerkin methods in their efficiency to reduce infinite dimensional systems, described by partial differential equations, to low dimensional systems of ordinary differential equations, both concerning the effort in their application and the accuracy of the resulting reduced system. Important questions like the choice of the form of the ansatz functions (modes), the choice of the number m of modes and, finally, the construction of the reduced system are addressed. For the latter point, both the linear or standard Galerkin method making use of the Karhunen Loeve (proper orthogonal decomposition) ansatz functions and the nonlinear Galerkin method, using approximate inertial manifold theory, are used. In addition, also the post-processing Galerkin method is compared with the other approaches. (C) 2001 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码:2131 / 2147
页数:17
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