• Nuclear Engineering and Technology
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• v.34 no.4
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• pp.314-322
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• 2002

A new extrapolation method is developed and applied to the additive angular dependent rebalance (AADR) acceleration for discrete ordinates neutron transport calculations. With this extrapolation, the convergence of AADR solution for distinct discretizations between the high- order and low-order equations is remarkably improved and thus the “inconsistent discretization problem” is resolved. Fourier analysis is also performed to find the optimal extrapolation and weighting parameters, which give the smallest spectral radius. The numerical tests demonstrate that the AADR with extrapolation works well as predicted by the Fourier analysis.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.156-161
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• 2003

It is an interest problem to predict substance distributions in three-dimensional space. Recently, a research field as Geostatistics is advanced. It is a kind of inter- or extrapolation mathematically. Some useful means for the inter- and extrapolation are known, in which slide window method with neural networks is hopeful one. We propose multi-dimensional extrapolation using multi-layer neural networks and the slide-window method. The multi-dimensional extrapolation is not similar to one-dimension. It has plural algorithms. We researched line predictors and local-plain predictors I two-dimensional space. The both predictors are equivalent; however, in multi-dimensional extrapolation, it is very important to find the direction of predictions. Especially, since the slide window method requires information to predict the future in sampling data, if they are not ordered appropriately in the direction, the predictor cannot operate. We tested the extrapolation for typical two-dimensional functions, and found an excellent character of slide-window method based on local-plain. By using the method, we can extrapolate the function until twice-outer regions of the definitions.

• Nuclear Engineering and Technology
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• v.15 no.1
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• pp.33-40
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• 1983

It is shown that the Shanks sequence $E_{k}$-transformation and the conventional extrapolation method are theoretically related. The $E_1$$^2$-transformation method is then applied for the multigroup diffusion problems. The diffusion code, CITATION, is modified for this study and the computing time is compared for each iteration tactics. The Equipose method, in which only sing1e inner iteration for each energy group is carried for an outer iteration, has been known as the fastest iteration method. However, in the case of 3-group problems, the proposed method, in which the number of inner iteration for the fast and thermal group is 2 and 1 respectively, gives better convergency than the Equipose method by about 12%. The double extrapolation method results in faster computing time than the single extrapolation method without computing storage problem. It is, however, to note that this method is verified only for a two-group treatment.t.

• International Journal of Aeronautical and Space Sciences
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• v.17 no.1
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• pp.64-72
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• 2016

The coverage area of a GNSS regional ionospheric delay model is mainly determined by the distribution of GNSS ground monitoring stations. Extrapolation of the ionospheric model data can extend the coverage area. An extrapolation algorithm, which combines observed ionospheric delay with the environmental parameters, is proposed. Neural network and least square regression algorithms are developed to utilize the combined input data. The bi-harmonic spline method is also tested for comparison. The IGS ionosphere map data is used to simulate the delays and to compute the extrapolation error statistics. The neural network method outperforms the other methods and demonstrates a high extrapolation accuracy. In order to determine the directional characteristics, the estimation error is classified into four direction components. The South extrapolation area yields the largest estimation error followed by North area, which yields the second-largest error.

• Geophysics and Geophysical Exploration
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• v.1 no.2
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• pp.116-126
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• 1998

I present a datuming scheme for poststack data that uses wavefield depth extrapolation. The method I have developed allows the use of any depth extrapolation technique, such as phase-shift, split-step, and finite-difference extrapolation. I derive the datuming algorithms by transposing and taking the complex conjugate (i.e. taking adjoint) of the corresponding forward modeling operator, which does upward extrapolation from a flat surface to an irregular surface. The exact adjoint relation between the forward modeling operator and the datuming operator is demonstrated algebraically. Testing the poststack datuming algorithms with synthetic data, using several depth extrapolation algorithms, has shown that the method works well.

• Nuclear Engineering and Technology
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• v.55 no.12
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• pp.4350-4356
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• 2023

Radiation detection systems working at high count rates suffer from the overlapping of their output electric pulses, known as pulse pile-up phenomenon, resulting in spectrum distortion and degradation of the energy resolution. Pulse tail extrapolation is a pile-up correction method which tries to restore the shifted baseline of a piled-up pulse by extrapolating the overlapped part of its preceding pulse. This needs a mathematical model which is almost always nonlinear, fitted usually by a nonlinear least squares (NLS) technique. NLS is an iterative, potentially time-consuming method. The main idea of the present study is to replace the NLS technique by an integration-based non-iterative method (NIM) for pulse tail extrapolation by an exponential model. The idea of linear extrapolation, as another non-iterative method, is also investigated. Analysis of experimental data of a NaI(Tl) radiation detector shows that the proposed non-iterative method is able to provide a corrected spectrum quite similar with the NLS method, with a dramatically reduced computation time and complexity of the algorithm. The linear extrapolation approach suffers from a poor energy resolution and throughput rate in comparison with NIM and NLS techniques, but provides the shortest computation time.

• Nuclear Engineering and Technology
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• v.50 no.7
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• pp.1043-1050
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• 2018

For an efficient Monte Carlo (MC) burnup analysis, an accurate high-order depletion scheme to consider the nonlinear flux variation in a coarse burnup-step interval is crucial accompanied with an accurate depletion equation solver. In a Seoul National University MC code, McCARD, the high-order depletion schemes of the quadratic depletion method (QDM) and the linear extrapolation/quadratic interpolation (LEQI) method and a depletion equation solver by the Chebyshev rational approximation method (CRAM) have been newly implemented in addition to the existing constant extrapolation/backward extrapolation (CEBE) method using the matrix exponential method (MEM) solver with substeps. In this paper, the quadratic extrapolation/quadratic interpolation (QEQI) method is proposed as a new high-order depletion scheme. In order to examine the effectiveness of the newly-implemented depletion modules in McCARD, four problems in the VERA depletion benchmarks are solved by CEBE/MEM, CEBE/CRAM, LEQI/MEM, QEQI/MEM, and QDM for gadolinium isotopes. From the comparisons, it is shown that the QEQI/MEM predicts ${k_{inf}}^{\prime}s$ most accurately among the test cases. In addition, statistical uncertainty propagation analyses for a VERA pin cell problem are conducted by the sensitivity and uncertainty and the stochastic sampling methods.

• Bulletin of the Korean Chemical Society
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• v.28 no.3
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• pp.386-390
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• 2007

By use of a simple two-point extrapolation scheme estimating the correlation energies of the molecules along with the basis sets specifically targeted for extrapolation, we have shown that the MP2 basis set limit binding energies of large hydrogen-bonded complexes can be accurately predicted with relatively small amount of computational cost. The basis sets employed for computation and extrapolation consist of the smallest correlation consistent basis set cc-pVDZ and another basis set made of the cc-pVDZ set plus highest angular momentum polarization functions from the cc-pVTZ set, both of which were then augmented by diffuse functions centered on the heavy atoms except hydrogen in the complex. The correlation energy extrapolation formula takes the (X+1)-3 form with X corresponding to 2.0 for the cc-pVDZ set and 2.3 for the other basis set. The estimated MP2 basis set limit binding energies for water hexamer, hydrogen fluoride pentamer, alaninewater, phenol-water, and guanine-cytosine base pair complexes of nucleic acid by this method are 45.2(45.9), 36.1(37.5), 10.9(10.7), 7.1(6.9), and 27.6(27.7) kcal/mol, respectively, with the values in parentheses representing the reference basis set limit values. A comparison with the DFT results by B3LYP method clearly manifests the effectiveness and accuracy of this method in the study of large hydrogen-bonded complexes.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.91-102
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• 1999

A new method is developed for estimating the mean of a population which has a linear trend. The suggested estimator is based on the balanced systematic sampling method and the concept of interpolation and extrapolation. The efficiency of the proposed method is compared with that of conventional methods.

• Journal of the Optical Society of Korea
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• v.18 no.5
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• pp.507-516
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• 2014

We present a hybrid method for spectral reflectivity recovery, using 3D extrapolation as a supplemental method for 3D interpolation. The proposed 3D extrapolation is an extended version of 3D interpolation based on the barycentric algorithm. It is faster and more accurate than the conventional spectral-recovery techniques of principal-component analysis and nonnegative matrix transformation. Four different extrapolation techniques (based on nearest neighbors, circumcenters, in-centers, and centroids) are formulated and applied to recover spectral reflectivity. Under the standard conditions of a D65 illuminant and 1964 $10^{\circ}$ observer, all reflectivity data from 1269 Munsell color chips are successfully reconstructed. The superiority of the proposed method is demonstrated using statistical data to compare coefficients of correlation and determination. The proposed hybrid method can be applied for fast and accurate spectral reflectivity recovery in image processing.