Solving Transient Nonlinear Heat Conduction Problems by Proper Orthogonal Decomposition and the Finite-Element Method

Fic, A.; Białecki, Ryszard A.; Kassab, Alain J.

doi:10.1080/10407790590935920

Cited by 80 publications

(55 citation statements)

References 16 publications

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“…Taking into account of these remarks, the problem given by (6) is transformed to the problem given by (8):…”

Section: Structure Of the Rm With The Mimmentioning

confidence: 99%

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Comparison between the modal identification method and the POD-Galerkin method for model reduction in nonlinear diffusive systems

Balima¹,

Favennec²,

Girault³

et al. 2006

Int. J. Numer. Meth. Engng

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SUMMARYThis paper presents a comparison between the modal identification method (MIM) and the proper orthogonal decomposition-Galerkin (POD-G) method for model reduction. An example of application on a nonlinear diffusive system is used to illustrate the study. The study shows that in both methods, the state formulation of the nonlinear diffusive equation may be similar. However, the ideas behind both methods are completely different. The considered example shows that, for both methods, reducing the order up to 99.5% gives enough accuracy to simulate the dynamic of the original system. It is also seen in this example that the reduced model given through the MIM are slightly faster and more accurate than the ones given through the POD-G method.

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“…Taking into account of these remarks, the problem given by (6) is transformed to the problem given by (8):…”

Section: Structure Of the Rm With The Mimmentioning

confidence: 99%

“…The basic idea of the MIM is to build a model that has the same form (8), but with a new state vector X r of order n N. Hence the RM writes:…”

mentioning

confidence: 99%

Comparison between the modal identification method and the POD-Galerkin method for model reduction in nonlinear diffusive systems

Balima¹,

Favennec²,

Girault³

et al. 2006

Int. J. Numer. Meth. Engng

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show abstract

“…This method has found applications in fluid dynamics [18], nonlinear heat transfer [16], MEMS [20,30], nonlinear structural systems [23,28], vibration and acoustic [5], structural health monitoring [29], control systems [4], climate modelling [14], stochastic PDEs [11], pattern recognition [24], etc. The POD method can be used for any complex linear as well as nonlinear system.…”

Section: Introductionmentioning

confidence: 99%

Application of multilevel scheme and two level discretization for POD based model order reduction of nonlinear transient heat transfer problems

Gaonkar

Kulkarni

2014

Comput Mech

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In the present paper, a method to reduce the computational cost associated with solving a nonlinear transient heat conduction problem is presented. The proposed method combines the ideas of two level discretization and the multilevel time integration schemes with the proper orthogonal decomposition model order reduction technique. The accuracy and the computational efficiency of the proposed methods is discussed. Several numerical examples are presented for validation of the approach. Compared to the full finite element model, the proposed method significantly reduces the computational time while maintaining an acceptable level of accuracy.

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“…Similar techniques have recently been applied in standard thermal conduction problems e.g. [1][2][3][4][5] though the general use of ROM for heat transfer is not yet widespread. One major difficulty with the development of ROM for general thermal analysis is the need to include the very nonlinear effects of enclosure radiation in many applications.…”

Section: Reduced Order Modelsmentioning

confidence: 99%

“…[1][2][3][4][5][6]. Here a simple sketch of the attributes and procedure is provided to introduce the method for the particular applications of interest.…”

Section: Overview Of Rommentioning

confidence: 99%

Solving Transient Nonlinear Heat Conduction Problems by Proper Orthogonal Decomposition and the Finite-Element Method

Cited by 80 publications

References 16 publications

Comparison between the modal identification method and the POD-Galerkin method for model reduction in nonlinear diffusive systems

Comparison between the modal identification method and the POD-Galerkin method for model reduction in nonlinear diffusive systems

Application of multilevel scheme and two level discretization for POD based model order reduction of nonlinear transient heat transfer problems

Reduced order models for thermal analysis : final report : LDRD Project No. 137807.

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