• Title/Summary/Keyword: adjoint

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Advanced two-level CMFD acceleration method for the 3D whole-core high-fidelity neutron adjoint transport calculation

  • Zhu, Kaijie;Hao, Chen;Xu, Yunlin
    • Nuclear Engineering and Technology
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    • v.53 no.1
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    • pp.30-43
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    • 2021
  • In the 2D/1D method, a global adjoint CMFD based on the generalized equivalence theory is built to synthesize the 2D radial MOC adjoint and 1D axial NEM adjoint calculation and also to accelerate the iteration convergence of 3D whole-core adjoint transport calculation. Even more important, an advanced yet accurate two-level (TL) CMFD acceleration technique is proposed, in which an equivalent one-group adjoint CMFD is established to accelerate the multi-group adjoint CMFD and then to accelerate the 3D whole-core adjoint transport calculation efficiently. Based on these method, a new code is developed to perform 3D adjoint neutron flux calculation. Then a set of VERA and C5G7 benchmark problems are chosen to verify the capability of the 3D adjoint calculations and the effectiveness of TL CMFD acceleration. The numerical results demonstrate that acceptable accuracy of 2D/1D adjoint calculations and superior acceleration of TL CMFD are achievable.

An Approximate Determination of the Adjoint Flux by the Borresen's Coarse-Mesh Method (Borresen의 소격해법에 의한Adjoint속의 근사적 결정)

  • Kim, Chang-Hyo
    • Nuclear Engineering and Technology
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    • v.21 no.1
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    • pp.56-61
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    • 1989
  • A simple, approximate method for determining the two-group adjoint flux based on the Borresen's coarse-mesh 1.5 group diffusion theory scheme is proposed. With the principle of the 1.5 group diffusion theory scheme, the method describes the thermal leakage term of the adjoint flux approximately by the geomerical buckling determined from the fast adjoint flux. The accuracy of the adjoint flux is investigated tv the comparison of the adjoint flux constructed from this method with a fine-mesh finite-difference KIDD computations. It is shown that the proposed method can predict the adjoint flux as good as the KIDD results. Possible applications of the present method are then suggested in conjunction with the application of the perturbation theory.

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Estimation of Optimal Weight in Tidal Modeling with the Adjoint Method (조석 모델링에서 adjoint 방법 적용시 적정 가중치 산정)

  • Lee, Jae-Hak;Park, Kyeong;Song, Yong-Sik
    • The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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    • v.5 no.3
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    • pp.177-185
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    • 2000
  • The adjoint method is a method of data assimilation to improve the model results by seeking for model parameters that minimize the cost function and satisfy the governing equations of a model simultaneously. An adjoint package was set up for the two-dimensional linear tidal model and was applied to an idealized domain for an optimal estimation of the open boundary conditions. The assimilating data were selected from the results of forward modeling. Attention is paid on the response of the adjoint package to weighting parameters, the importance of initial estimates of model parameters and the applicability of the adjoint package to the case with varying depth. A procedure to determine optimal weight is presented based on the relationships between weights and other factors.

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AERODYNAMIC SENSITIVITY ANALYSIS FOR NAVIER-STOKES EQUATIONS

  • Kim, Hyoung-Jin;Kim, Chongam;Rho, Oh-Hyun;Lee, Ki Dong
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.3 no.2
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    • pp.161-171
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    • 1999
  • Aerodynamic sensitivity analysis codes are developed via the hand-differentiation using a direct differentiation method and an adjoint method respectively from discrete two-dimensional compressible Navier-Stokes equations. Unlike previous other researches, Baldwin-Lomax algebraic turbulence model is also differentiated by hand to obtain design sensitivities with respect to design variables of interest in turbulent flows. Discrete direct sensitivity equations and adjoint equations are efficiently solved by the same time integration scheme adopted in the flow solver routine. The required memory for the adjoint sensitivity code is greatly reduced at the cost of the computational time by allowing the large banded flux jacobian matrix unassembled. Direct sensitivity code results are found to be exactly coincident with sensitivity derivatives obtained by the finite difference. Adjoint code results of a turbulent flow case show slight deviations from the exact results due to the limitation of the algebraic turbulence model in implementing the adjoint formulation. However, current adjoint sensitivity code yields much more accurate sensitivity derivatives than the adjoint code with the turbulence eddy viscosity being kept constant, which is a usual assumption for the prior researches.

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ON ADJOINT CURVES OF FRAMED CURVES AND SOME RULED SURFACES

  • Bahar Dogan Yazici;Siddika Ozkaldi Karakus;Murat Tosun
    • Honam Mathematical Journal
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    • v.45 no.3
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    • pp.380-396
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    • 2023
  • In this study, we introduce the adjoint curves of framed curves. We examine some characterizations of adjoint curve of a framed curve. In addition, we give the conditions for framed curves and adjoint curves to be Bertrand and Mannheim curves. Then, we introduce adjoint curves of Frenet-type framed curves and give ruled surfaces related to adjoint curves. Finally, we create normal and binormal surfaces of the framed adjoint curves and obtain some characterizations of these surfaces and we support by the results with figures.

A Robustness Improvement of Adjoint-LMS Algorithms for Active Noise Control (능동소음제어를 위한 Adjoint-LMS 알고리즘의 강인성 개선)

  • Moon, Hak-ryong;Shon, Jin-geun
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.65 no.3
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    • pp.171-177
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    • 2016
  • Noise problem that occurs in living environment is a big trouble in the economic, social and environmental aspects. In this paper, the filtered-X LMS algorithms, the adjoint LMS algorithms, and the robust adjoint LMS algorithms will be introduced for applications in active noise control(ANC). The filtered-X LMS algorithms is currently the most popular method for adapting a filter when the filter exits a transfer function in the error path. The adjoint LMS algorithms, that prefilter the error signals instead of divided reference signals in frequency band, is also used for adaptive filter algorithms to reduce the computational burden of multi-channel ANC systems such as the 3D space. To improve performance of the adjoint LMS ANC system, an off-line measured transfer function is connected parallel to the LMS filter. This parallel-fixed filter acts as a noise controller only when the LMS filter is abnormal condition. The superior performance of the proposed system was compared through simulation with the adjoint LMS ANC system when the adaptive filter is in normal and abnormal condition.

Adjoint Design Sensitivity Analysis of Damped Systems (보조변수법을 이용한 감쇠계 고유치 설계민감도 해석)

  • Yoo, Jung-Hoon;Lee, Tae-Hee
    • Proceedings of the KSME Conference
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    • 2001.06c
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    • pp.398-401
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    • 2001
  • There are two methods to calculate design sensitivity such as direct differentiation method and adjoint method. A sort of direct differentiation method for design sensitivity analysis costs too much when number of design variables is much larger than the number of response functions whose design sensitivity analyses are required. Therefore, an adjoint method is suggested for the case that the dimension of design variables is lager than the number of response function. An adjoint method is required to compute adjoint variables from the simultaneous linear system equation, the so-called adjoint equation, requiring only the eigenvalue and its associated eigenvectors for mode being differentiated. This method has been extended to the repeated eigenvalue problem. In this paper, we propose an adjoint method for deign sensitivity analysis of damped vibratory systems with distinct eigenvalues.

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Mathematical Adjoint Solution to Analytic Function Expansion Nodal (AFEN) Method (해석함수전개 노달방법의 수학적 수반해)

  • Cho, Nam-Zin;Hong, Ser-Gi
    • Nuclear Engineering and Technology
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    • v.27 no.3
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    • pp.374-384
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    • 1995
  • The mathematical adjoint solution of the Analytic Function Expansion (AFEN) method is found by solving the transposed matrix equation of AFEN nodal equation with only minor modification to the forward solution code AFEN. The perturbation calculations are then performed to estimate the change of reactivity by using the mathematical adjoint The adjoint calculational scheme in this study does not require the knowledge of the physical adjoint or the eigenvalue of the forward equation. Using the adjoint solutions, the exact and first-order perturbation calculations are peformed for the well-known benchmark problems (i.e., IAEA-2D benchmark problem and EPRI-9R benchmark problem). The results show that the mathematical adjoint flux calculated in the code is the correct adjoint solution of the AFEN method.

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Forecast Sensitivity Analysis of An Asian Dust Event occurred on 6-8 May 2007 in Korea (2007년 5월 6-8일 황사 현상의 예측 민감도 분석)

  • Kim, Hyun Mee;Kay, Jun Kyung
    • Atmosphere
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    • v.20 no.4
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    • pp.399-414
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    • 2010
  • Sand and dust storm in East Asia, so called Asian dust, is a seasonal meteorological phenomenon. Mostly in spring, dust particles blown into atmosphere in the arid area over northern China desert and Manchuria are transported to East Asia by prevailing flows. An Asian dust event occurred on 6-8 May 2007 is chosen to investigate how sensitive the Asian dust transport forecast to the initial condition uncertainties and to interpret the characteristics of sensitivity structures from the viewpoint of dynamics and predictability. To investigate the forecast sensitivities to the initial condition, adjoint sensitivities that calculate gradient of the forecast aspect (i.e., response function) with respect to the initial condition are used. The forecast aspects relevant to Asian dust transports are dry energy forecast error and lower tropospheric pressure forecast error. The results show that the sensitive regions for the dry energy forecast error and the lower tropospheric pressure forecast error are initially located in the vicinity of the trough and then propagate eastward as the surface low system moves eastward. The vertical structures of the adjoint sensitivities for the dry energy forecast error are upshear tilted structures, which are typical adjoint sensitivity structures for extratropical cyclones. Energy distribution of singular vectors also show very similar structures with the adjoint sensitivities for the dry energy forecast error. The adjoint sensitivities of the lower tropospheric pressure forecast error with respect to the relative vorticity show that the accurate forecast of the trough (or relative vorticity) location and intensity is essential to have better forecasts of the Asian dust event. Forecast error for the atmospheric circulation during the dust event is reduced 62.8% by extracting properly weighted adjoint sensitivity perturbations from the initial state. Linearity assumption holds generally well for this case. Dynamics of the Asian dust transport is closely associated with predictability of it, and the improvement in the overall forecast by the adjoint sensitivity perturbations implies that adjoint sensitivities would be beneficial in improving the forecast of Asian dust events.