Exact-to-precision generalized perturbation theory for source-driven systems

Wang, Congjian; Abdel-Khalik, Hany S.

doi:10.1016/j.nucengdes.2011.09.009

Cited by 9 publications

(11 citation statements)

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“…The comparison between sb-ROM method and the go-ROM-GOP method has been published previously (Wang and Abdel-Khalik, 2011). For the sake of a complete discussion, we briefly discuss it here and refer the reader to previous publications.…”

Section: Overview Of Go-rom-gop Methodsmentioning

confidence: 99%

“…In another go-ROM-GOP method (Greenspan and Gilai, 1978), the number of adjoint executions depends on n O−1 , where O is the order of variation and n in the number of input parameters. In a previous publication (Wang and Abdel-Khalik, 2011), the sb-ROM method was compared to the go-ROM-GOP method in Mckinley and Rahnema. While both methods are shown to produce the exact response variations within machine precision, the computational cost for both methods is significantly different.…”

Section: Overview Of New Developmentsmentioning

confidence: 99%

“…The next few subsections introduce the three steps of the sb-ROM method and apply them to an LTI problem. Since application to GOP problem was published elsewhere (Wang and Abdel-Khalik, 2011), only differences to the LTI problem will be briefly discussed.…”

Section: Mathematical Descriptionmentioning

confidence: 99%

“…For go-ROM-GOP problems, the previous work has shown that this simple idea applied here to LTI problems could be extended to find an active subspace that captures nonlinear state variations (Wang and Abdel-Khalik, 2011). In doing so, the active subspace represents all directions in the input parameters space that give rise to all orders of variations for the state.…”

Section: If the Condition Inmentioning

confidence: 99%

“…Further, it will be compared to a typical go-ROM-LTI algorithm, in particular the one-shot algorithm developed in Antoulas and colleagues (2001) and Bui-Thanh and colleagues (2006). Given that previous work has applied the sb-ROM method to GOP problems (Wang and Abdel-Khalik, 2011), a brief mathematical description along with one demonstrative example of the GOP problem will be recalled in this manuscript for the sake of a complete discussion.…”

Section: Introductionmentioning

confidence: 99%

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State-Based Adjoint Method for Reduced Order Modeling

Bang

Wang

Abdel-Khalik

2012

Transport Theory and Statistical Physics

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Introduced here is an adjoint state-based method for model reduction, which provides a single solution to two classes of reduction methods that are currently in the literature. The first class, which represents the main subject of this manuscript, is concerned with linear time invariant problems where one is interested in calculating linear responses variations resulting from initial conditions perturbations. The other class focuses on perturbations introduced in the operator, which result in nonlinear responses variations. Unlike existing adjoint-based methods where an adjoint function is calculated based on a given response, the state-based method employs the state variations to set up a number of adjoint problems, each corresponding to a pseudoresponse. This manuscript extends the applicability of state-based method to generate reduced order models for linear time invariant problems. Previous developments focusing on operator perturbations are reviewed briefly to highlight the common features of the state-based algorithm as applied to these two different classes of problems. Similar to previous developments, the state-based reduction is shown to set an upper-bound on the maximum discrepancy between the reduced and original model predictions. The methodology is applied and compared to other state-of-the-art methods employing several nuclear reactor diffusion and transport models.

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Section: Overview Of Go-rom-gop Methodsmentioning

confidence: 99%

Section: Overview Of New Developmentsmentioning

confidence: 99%

Section: Mathematical Descriptionmentioning

confidence: 99%

Section: If the Condition Inmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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