• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.29 no.6 s.237
• /
• pp.703-710
• /
• 2005

A finite element discretization of the advection and redistancing equations of level set method has been studied. It has been shown that Galerkin spatial discretization combined with Crank-Nicolson temporal discretization of the advection equation of level set yields a good result and that consistent streamline upwind Petrov-Galerkin(CSUPG) discretization of the redistancing equation gives satisfactory solutions for two test problems while the solutions of streamline upwind Petrov-Galerkin(SUPG) discretization are dissipated by the numerical diffusion added for the stability of a hyperbolic system. Furthermore, it has been found that the solutions obtained by CSUPG method are comparable to those by second order ENO method.

• Communications for Statistical Applications and Methods
• /
• v.18 no.1
• /
• pp.89-102
• /
• 2011

The discretization process that converts continuous attributes into discrete ones is a preprocessing step in data mining such as classification. Some classification algorithms can handle only discrete attributes. The purpose of discretization is to obtain discretized data without losing the information for the original data and to obtain a high predictive accuracy when discretized data are used in classification. Many discretization algorithms have been developed. This paper presents the results of our comparative study on recently proposed representative discretization algorithms from the view point of splitting versus merging and supervised versus unsupervised. We implemented R codes for discretization algorithms and made them available for public users.

• The Pure and Applied Mathematics
• /
• v.13 no.1 s.31
• /
• pp.19-38
• /
• 2006

We analyze the spectral collocation approximation for a parabolic partial integrodifferential equations(PIDE) with a weakly singular kernel. The space discretization is based on the spectral collocation method and the time discretization is based on Crank-Nicolson scheme with a graded mesh. We obtain the stability and second order convergence result for fully discrete scheme.

• East Asian mathematical journal
• /
• v.30 no.5
• /
• pp.609-616
• /
• 2014

In this paper we consider hyperbolic equations related to the p-Laplacian with a nonsmooth kernel. By exploiting a suitable implicit time-discretization technique we obtain the existence of global strong solution.

• East Asian mathematical journal
• /
• v.26 no.3
• /
• pp.403-413
• /
• 2010

In this paper, we consider a doubly nonlinear parabolic equation related to the Leray-Lions operator with Dirichlet boundary condition and initial data given. By exploiting a suitable implicit time-discretization technique, we obtain the existence of global strong solution.

• 제어로봇시스템학회:학술대회논문집
• /
• 2005.06a
• /
• pp.2562-2567
• /
• 2005

This paper suggests a new method discretization of nonlinear system using Taylor series expansion and zero-order hold assumption. This method is applied into the sampled-data representation of a nonlinear system with input time delay. Additionally, the delayed input is time varying and its amplitude is bounded. The maximum time-delayed input is assumed to be two sampling periods. Them mathematical expressions of the discretization method are presented and the ability of the algorithm is tested for some of the examples. And 'hybrid' discretization scheme that result from a combination of the ‘scaling and squaring' technique with the Taylor method are also proposed, especially under condition of very low sampling rates. The computer simulation proves the proposed algorithm discretized the nonlinear system with the variable time-delayed input accurately.

• 유체기계공업학회:학술대회논문집
• /
• 2000.12a
• /
• pp.285-292
• /
• 2000

Numerical calculation is applied to centrifugal pump at design condition by using commercial code STAR-CD and Tascflow, and these results are compared with experimental data at impeller outlet. Numerical analysis is also performed by changing turbulence model and discretization scheme at design condition using Tascflow. Turbulence model and discretization scheme used to Tascflow are k-$\epsilon$, k-$\omega$ turbulence model and upwind, modified linear profile scheme. W;th the same turbulence model and discretization scheme, two results of STAR-CD and Tascflow are very similar. But there is significant difference in numerical results near hub and shroud of impeller with different kinds of turbulent model and discretization scheme at design condition. And with k- $\omega$ turbulence model and modified linear profile scheme, it is showed that numerical results are very similar to experimental results of impeller outlet

• Journal of Mechanical Science and Technology
• /
• v.20 no.7
• /
• pp.950-960
• /
• 2006

An output time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via a digital computer. A new method for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed in this paper. This method is applied to the sampled-data representation of a nonlinear system with a constant output time-delay. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. In addition, 'hybrid' discretization schemes resulting from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. A performance of the proposed method is evaluated using two nonlinear systems with time-delay output.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.22 no.1
• /
• pp.95-102
• /
• 2014

This paper presents zero crossing point(ZCP) estimation methods considering discretization error for a high speed brushless DC(BLDC) motor drive. The ZCP is estimated by detecting the change of back-EMF polarity for the BLDC sensorless drive, and the discretization error exist on the estimated ZCP. The discretization error of the ZCP is a cause of the delay of a commutation timing of current and increment of a current ripple factor. Besides a delay of a ZCP estimation brings on the limitation of a speed range for the BLDC sensorless drive. The compensation method based on the error analysis with probability theory for reducing the effects of the discretization error of the ZCP is proposed. Also a ZCP estimation method according to the Back-EMF patterns is proposed to widen the speed range for the BLDC sensorless drive. The proposed methods are verified by the experiment.

• Journal of Mechanical Science and Technology
• /
• v.19 no.11
• /
• pp.1975-1987
• /
• 2005

An input time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via digital computers. In this paper a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed. The mathematical structure of the new discretization method is analyzed. On the basis of this structure the sampled-data representation of nonlinear systems with time-delayed multi-input is presented. The delayed multi-input general equation has been derived. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. Additionally, hybrid discretization schemes that result from a combination of the scaling and squaring technique (SST) with the Taylor series expansion are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method's parameters to meet CPU time and accuracy requirements, are examined as well. A performance of the proposed method is evaluated using a nonlinear system with time delay maneuvering an automobile.