• Journal of the Korea Society of Computer and Information
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• v.3 no.4
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• pp.55-62
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• 1998

This Paper proposed a systolic Arrays architecture for computing Romberg's integration method. It consists of systolic arrays of two stage, one for integration by Trapezoidal rule and the other for integration by using Richardson's extrapolation. the proposed its architecture is very high speed and regular. This paper illustrates how " mathematical hardware " package, as well as software library routines, may be part of the mathematical problem solver's tool kit in the future.he future.

• 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.

• Proceedings of the Korean Nuclear Society Conference
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• 1997.05b
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• pp.566-570
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• 1997

The effect of average gamma energy on the external radiation dose has been analyzed. Cloud- and groundshine have been calculated according to the average gamma energy. Monte Carlo integration method was used for the calculation of cloudshine and Romberg quadrature method was adopted for groundshine. The analysis shows that the external gamma exposure is strong]y dependent on the gamma energy and the distribution of radiation sources.

• Journal of Electrical Engineering and Technology
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• v.8 no.4
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• pp.872-878
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• 2013

In industrial control systems, flow measurement is a very important issue. It is frequently needed to calculate how much total fluid or gas flows through a cross-section. Flow volume measurement tools use simple sampling or rectangle methods. Actually, flow volume measurement process is an integration process. For this reason, measurement systems using instantaneous sampling technique cause considerably high errors. In order to make more accurate flow measurement, numerical integration methods should be used. Literally, for numerical integration method, Rectangular, Trapezoidal, Simpson, Romberg and Gaussian Quadrature methods are suggested. Among these methods, trapezoidal rule method is quite easy to calculate and is notably more accurate and contains no restrictive conditions. Therefore, it is especially convenient for the portable flow volume measurement systems. In this study, the volume measurement of air which is flowing through a cross-section is achieved by using PLC ladder diagram. The measurements are done using two different approaches. Trapezoidal rule method is proposed to measure the flow sensor signal to minimize measurement errors due to the classical sampling method as a different approach. It is concluded that the trapezoidal rule method is more effective than the classical sampling.

• Progress in Superconductivity and Cryogenics
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• v.19 no.1
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• pp.51-55
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• 2017

To obtain Nuclear Magnetic Resonance (NMR) measurement of membrane protein, an NMR magnet is required to generate high intensity, homogeneity, and stability of field. A High-Temperature Superconducting (HTS) magnet is a promising alternative to a conventional Low-Temperature Superconducting (LTS) NMR magnet for high field, current density, and stability margin. Conventionally, an HTS coil has been wound by several winding techniques such as Single-Pancake (SP), Double-Pancake (DP), and layer-wound. The DP winding technique has been frequently used for a large magnet because long HTS wire is generally difficult to manufacture, and maintenance of magnet is convenient. However, magnetic field generated by the slanted turns and the splice leads to field inhomogeneity in Diameter of Spherical Volume (DSV). The field inhomogeneity degrades performance of NMR spectrometer and thus effect of the slanted turns and the splice should be analyzed. In this paper, field gradient of HTS double-pancake coils considering the slanted turns and the splice was calculated using Biot-Savart law and numerical integration. The calculation results showed that magnetic field produced by the slanted turns and the splice caused significant inhomogeneity of field.

• Journal of Biomedical Engineering Research
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• v.5 no.1
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• pp.9-14
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• 1984

The asymptotic solution using the Tailor series has been given explicit form for the solute concentration and overall solute removal in hemodiafilter using one dimensional model. The numerical solutions have been calculated within 0.001% error by the Romberg integration method. Compared with the numerical solutions, the oneterm asymptotic solutions were found to be within 3% error for the condition > 3.0 and three-terms asymtotic solutions were required for the condition >0.7 where denotes measure of convection over diffusional transport and a the ratio of blood flow rate over dialysate flow rate.

• International Journal of Automotive Technology
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• v.8 no.5
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• pp.563-573
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• 2007

Optimal design of an automotive catalytic converter for minimization of cold-start emissions is numerically performed using a micro genetic algorithm for two optimization problems: optimal geometry design of the monolith for various operating conditions and optimal axial catalyst distribution. The optimal design process considered in this study consists of three modules: analysis, optimization, and control. The analysis module is used to evaluate the objective functions with a one-dimensional single channel model and the Romberg integration method. It obtains new design variables from the control module, produces the CO cumulative emissions and the integral value of a catalyst distribution function over the monolith volume, and provides objective function values to the control module. The optimal design variables for minimizing the objective functions are determined by the optimization module using a micro genetic algorithm. The control module manages the optimal design process that mainly takes place in both the analysis and optimization modules.