A note on equivalence of proper orthogonal decomposition methods

Wu, Chunguo; Liang, Yanchun; Lin, W. Z.; Lee, H.P.; Lim, Siak Piang

doi:10.1016/s0022-460x(03)00032-4

Cited by 67 publications

(30 citation statements)

References 11 publications

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“…The mathematical theory and computational procedures related to POD have origins remote in time and in application fields, and are now presented in a vast and still growing literature, of which we mention [Chatterjee 2000;Wu et al 2003;Ostrowski et al 2008]. Here only the specific procedure selected and applied to the present purposes is outlined, without analytical details.…”

Section: Introductionmentioning

confidence: 99%

Diagnosis of concrete dams by flat-jack tests and inverse analyses based on proper orthogonal decomposition

Garbowski

Maier

Novati

2011

J. Mech. Mater. Struct.

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Dedicated to the memory of Marie-Louise Steele and to Charles Steele.Flat-jack tests have been employed for decades for the assessment of stresses and Young moduli in possibly deteriorated concrete dams and masonry structures. We propose a procedure for such tests that includes several innovations: identification of Young moduli and shear modulus in the presence of orthotropy, of pre-existing normal and shear stresses, and of tensile and compressive strength and fracture energy; use of full-field displacement measurements by digital image correlation (instead of extensometers); computer simulations performed once-and-for-all and productive of results which are subsequently processed out by proper orthogonal decomposition and its truncation; and identification of parameters in situ, soon after the tests, by portable computer with software able to perform inverse analyses by mathematical tools newly introduced into this context. The proposed procedure is validated by means of pseudoexperimental numerical exercises, by employing comparatively, as central computational tools, artificial neural networks and a trust region algorithm implying only first-order derivatives (with respect to the sought parameters) of the discrepancy function to minimize.

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Section: Introductionmentioning

confidence: 99%

Diagnosis of concrete dams by flat-jack tests and inverse analyses based on proper orthogonal decomposition

Garbowski

Maier

Novati

2011

J. Mech. Mater. Struct.

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“…A proper orthogonal decomposition (POD) of a numerical solution (or, in general, of a given set of data, see, e.g., [5,6,7]) consists of finding a set of basis functions (orthogonal w.r.t. a given scalar product) which, even containing a small number of elements, can represent sufficiently well the numerical solution.…”

Section: Proper Orthogonal Decomposition (Pod)mentioning

confidence: 99%

Atlas-Based Reduced Models of Blood Flows for Fast Patient-Specific Simulations

McLeod

Caiazzo

Fernández

et al. 2010

Statistical Atlases and Computational Models of the Heart

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Abstract.Model-based interpretation of the complex clinical data now available (shape, motion, flow) can provide quantitative information for diagnosis as well as predictions. However such models can be extremely time consuming, which does not always fit with the clinical time constraints. The aim of this work is to propose a model reduction technique to perform faster patient-specific simulations with prior knowledge built from simulations on an average anatomy. Rather than simulating a full fluid problem on individual patients, we create a representative 'template' of the artery shape. A full flow simulation is carried out only on this template, and a reduced model is built from the results. Then this reduced model can be transported to the individual geometries, allowing faster computational analysis. Here we propose a preliminary validation of this idea. A well-posed framework based on currents representation of shapes is used to create an unbiased template of the pulmonary artery for 4 patients with Tetralogy of Fallot. Then, a reduced computational fluid dynamics model is built on this template. Finally, we demonstrate that this reduced model can represent a specific patient simulation.

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“…So, if a predefined global projection matrix is used, the basis vector updates will be avoided. For the two reasons, the improved algorithm introduces a preliminary LP selection procedure and constructs projection matrix by the proper orthogonal decomposition (POD) method [22]. Compared with the original method, the improved method takes less time to extract a ROM of similar quality and gets some other benefits.…”

Section: Introductionmentioning

confidence: 99%

A Two-Step Global Maximum Error Controller-Based TPWL MOR with POD Basis Vectors and Its Applications to MEMS

Liu

Wang

2017

Mathematical Problems in Engineering

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In our previous study, we have proposed a linearization point (LP) selection method based on a global maximum error controller for the trajectory piecewise-linear (TPWL) method. It has been demonstrated that this method has many advantages over other existing methods. In this paper, a more efficient version of this method is presented, which introduces a preliminary LP selection procedure and constructs projection matrix by the proper orthogonal decomposition (POD) method. Compared with the original method, the improved method takes much less time for extracting a reduced-order model (ROM) of similar quality and gets some other benefits (such as being easier to implement, having lower memory requirement, and enhanced flexibility). The effectiveness of the new method is fully demonstrated by a diode transmission line RLC circuit. And then, the method is applied to three more complicated microelectromechanical systems (MEMS) devices, which are a micromachined switch, an electrostatic micropump diaphragm, and a thermomechanical in-plane microactuator.

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A note on equivalence of proper orthogonal decomposition methods

Cited by 67 publications

References 11 publications

Diagnosis of concrete dams by flat-jack tests and inverse analyses based on proper orthogonal decomposition

Diagnosis of concrete dams by flat-jack tests and inverse analyses based on proper orthogonal decomposition

Atlas-Based Reduced Models of Blood Flows for Fast Patient-Specific Simulations

A Two-Step Global Maximum Error Controller-Based TPWL MOR with POD Basis Vectors and Its Applications to MEMS

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