• Structural Engineering and Mechanics
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• v.55 no.4
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• pp.885-900
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• 2015

This paper introduces Romberg-Richardson's method as one of the numerical integration tools for computation of stress intensity factor in a pre-cracked specimen subjected to a complex stress field across the crack faces. Also, the computation of stress intensity factor for various stress fields using existing three methods: average stress over interval method, piecewise linear stress method, piecewise quadratic method are modified by using Richardson extrapolation method. The direct integration method is used as reference for constant and linear stress distribution across the crack faces while Gauss-Chebyshev method is used as reference for nonlinear distribution of stress across the crack faces in order to obtain the stress intensity factor. It is found that modified methods (average stress over intervals-Richardson method, piecewise linear stress-Richardson method, piecewise quadratic-Richardson method) yield more accurate results after a few numbers of iterations than those obtained using these methods in their original form. Romberg-Richardson's method is proven to be more efficient and accurate than Gauss-Chebyshev method for complex stress field.

• ETRI Journal
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• v.39 no.3
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• pp.326-335
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• 2017

In the uplink transmission of massive (or large-scale) multi-input multi-output (MIMO) systems, large dimensional signal detection and its hardware design are challenging issues owing to the high computational complexity. In this paper, we propose low-complexity hardware architectures of Richardson iterative method-based massive MIMO detectors. We present two types of massive MIMO detectors, directly mapped (type1) and reformulated (type2) Richardson iterative methods. In the proposed Richardson method (type2), the matrix-by-matrix multiplications are reformulated to matrix-vector multiplications, thus reducing the computational complexity from $O(U^2)$ to O(U). Both massive MIMO detectors are implemented using a 65 nm CMOS process and compared in terms of detection performance under different channel conditions (high-mobility and flat fading channels). The hardware implementation results confirm that the proposed type1 Richardson method-based detector demonstrates up to 50% power savings over the proposed type2 detector under a flat fading channel. The type2 detector indicates a 37% power savings compared to the type1 under a high-mobility channel.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2014.11a
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• pp.53-55
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• 2014

본 논문에서는 deconvolution 알고리즘 중에 하나인 Richardson-Lucy deconvolution 의 개선된 알고리즘을 제시한다. Richardson-Lucy deconvolution 의 단점인 반복횟수가 증가할수록 노이즈도 같이 증폭되는 현상을 소개하고 이를 개선하기 위해 기존 알고리즘에 전, 후처리 필터를 이용하여 노이즈 증폭을 억제한다. 또한 다른 노이즈 증폭을 억제하는 알고리즘과 제안된 알고리즘의 비교를 통해서 제안된 알고리즘의 성능을 보여준다.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.567-584
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• 2014

In this paper, we consider approximation of eigenelements of a two dimensional compact integral operator with a smooth kernel by discrete collocation and iterated discrete collocation methods. By choosing numerical quadrature appropriately, we obtain convergence rates for gap between the spectral subspaces, and also we obtain superconvergence rates for eigenvalues and iterated eigenvectors. We then apply Richardson extrapolation to obtain further improved error bounds for the eigenvalues. Numerical examples are presented to illustrate theoretical estimates.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.679-702
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• 2014

Investigation of the numerical solution of singularly perturbed turning point problems dates back to late 1970s. However, due to the presence of layers, not many high order schemes could be developed to solve such problems. On the other hand, one could think of applying the convergence acceleration technique to improve the performance of existing numerical methods. However, that itself posed some challenges. To this end, we design and analyze a novel fitted operator finite difference method (FOFDM) to solve this type of problems. Then we develop a fitted mesh finite difference method (FMFDM). Our detailed convergence analysis shows that this FMFDM is robust with respect to the singular perturbation parameter. Then we investigate the effect of Richardson extrapolation on both of these methods. We observe that, the accuracy is improved in both cases whereas the rate of convergence depends on the particular scheme being used.

• 전자공학회논문지 IE
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• v.49 no.2
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• pp.75-81
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• 2012

In this paper, restoration methods were applied to restore analog medicine images with an aged image added and then blurred by noises. To restore the aged image blurred by the blurring function and added by noises, it was applied to the restoration methods which are inverse filtering and wiener filtering which are linear restoration techniques and Lucy-Richardson's algorithm which is nonlinear restoration technique. Moreover, ROC curve, a subjective evaluation method, was applied to evaluate the image quality of the restoration image. The wiener filtering using the ratio of constants acquired better image than the inverse filtering, but both of them couldn't improve ability to make a diagnosis. The restoration image applied to Lucy-Richardson algorithm was the best performance of the applied techniques and its sensitivity and specitivity were improved by 15[%] as much performance as the original aged image.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2015.11a
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• pp.114-117
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• 2015

본 논문에서는 Non-blind 디컨벌루션 알고리듬 중 하나인 Richardson-Lucy(RL) 디컨벌루션을 영상 분할을 통해 성능을 향상시킨 알고리듬을 제안한다. RL 디컨벌루션은 영상의 크기가 커질수록 연산 양이 크게 증가한다. 따라서 크기가 큰 영상의 RL 디컨벌루션은 계산에 많은 시간을 필요로 한다. 이를 개선하기 위하여 영상을 적절한 크기로 분할하여 각각 RL 디컨벌루션을 계산한다. 또한 분할 시 생기는 왜곡을 줄이기 위해 리플 제거를 위한 알고리듬을 추가한다. 이를 통해 기존의 알고리듬보다 연산 양을 줄여 빠른 RL 디컨벌루션이 가능하도록 개선한다.

• Water for future
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• v.22 no.2
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• pp.233-239
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• 1989

The partial differential equation of the groundwater flow was reduced to an ordinary differential equation by the Boltzmann transformation. Its numerical solutions were obtained by the finite difference method and the new method to get the initial missing slope using the Richardson method and the finite difference equation was proposed. The solutions computed by the newly proposed method were compared with investigator's computations and they showed a satisfactory agreement and that the proposed method is easy and simple to get solutions.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.6B
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• pp.499-505
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• 2011

The mixing behavior of turbidity currents in a reservoir is closely related with the annual temperature change of the reservoir. In the summer, the reservoir has a well defined structure: one or two thermoclines and some layers of different densities. This density stratification inhibits vertical mixing and affects various hydrodynamic processes within the reservoir. Therefore, many reservoirs can be operated to release water of the specific quality with the selective withdrawal. In this study, the hydraulic experiments were performed to analyze the efficiency of selective withdrawal. The velocity distributions are measured with PIV in the stratified tank with the "two-tank" method. The relationship between the Richardson number and the selective withdrawal efficiency are provided using the measured velocity distributions.

• Journal of Korean Society for Atmospheric Environment
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• v.12 no.4
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• pp.369-376
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• 1996

Major atmospheric stability classification methods were evaluated with meteorological data obtained by scoustic sounding profiler (SODAR/RASS) in Seoul. The Psequill classificatio method, the method most widely used because of its good agreement in respect of synoptic scope under the steady state, fails to describe the time lag, the response time on stability by heating or cooling caused by daily insolation or noctrunal surface radiation. Horizontal and vertical standard deviation of wind fluctuation $(\sigma_A and \sigma_E)$ method tend to classify night-time stable condition (E, F class) into unstable condition (A, B class). The classification matrix tables for Vogt's vertical temperature difference and wind speed using method ($\Delta$T $\cdot$ U) and bulk Richardson number (Rb) were amended for practical use over Seoul. The modified tables for $\Delta$T $\cdot$ U and Rb method were made by using comprehensive frequency distribution from Pasquill's method and other existing results, and the correlation coefficient(r) was equal to 0.829. It was confirmed that atmospheric stability could be changed with monitoring site characteristics, height and vertical difference between sensors of monitoring station, and classification method itself.