About the POD model reduction in computational mechanics for nonlinear continuous dynamical systems

R. Sampaio (1) , Christian Soize (2)

1 PUC Rio - Department of Mechanical Engineering
2 LaM - Laboratoire de Mécanique

An analysis of the efficiency of the reduced models constructed using the POD basis and the LIN-basis is presented in nonlinear dynamics for continuous elastic systems discretized by the finite element method. The POD-basis is the basis constructed with the POD method while the LIN-basis is the basis derived from the generalized eigenvalue problem associated with the underlying linear conservative part of the system and usually called the eigenmodes of vibration. The efficiency of the POD-basis or the LIN-basis is related to the speed of convergence in the frequency domain of the solution constructed with the reduced model with respect to its dimension. A basis will be more efficient than another if it converges more rapidly than the other. An example is presented in order to analyze the efficiency of the POD-and LIN-bases. It is concluded that the POD-basis is not more efficient than the LIN-basis for the example treated in nonlinear elastodynamics.

Mots clés: POD; proper orthogonal decomposition; model reduction; computational mechanics; nonlinear dynamical systems

Domaines: Mécanique [physics.med-ph]; Vibrations [physics.class-ph]; Vibrations [physics.class-ph]

R. Sampaio, Christian Soize. About the POD model reduction in computational mechanics for nonlinear continuous dynamical systems. International Conference on Computational and Experimental Engineering and Sciences, Jan 2007, Miami, United States. pp.Pages: 61-67. ⟨hal-00689705⟩