• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.345-362
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• 1998

We introduce and anlyze a naturally parallelizable frequency-domain method for parabolic problems with a Neumann boundary condition. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution of the original problem in the space-time domain. Existence and uniqueness of a solution of the transformed problem corresponding to each frequency is established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to solutions fo transformed problems and full error estimates for solving the given problem using a discrete Fourier inverse transform are given.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.2
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• pp.138-143
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• 2006

This paper presents intelligent digital redesign method for hybrid state space fuzzy-model-based controllers. For effectiveness and stabilization of continuous-time uncertain nonlinear systems under discrete-time controller, Takagi-Sugeno(TS) fuzzy model is used to represent the complex system. And global approach design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between nonlinearly interpolated linear operators to be matched. Also, by using the bilinear and inverse bilinear approximation method, we analyzed nonlinear system's uncertain parts more precisely. When a sampling period is sufficiently small, the conversion of a continuous-time structured uncertain nonlinear system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the global state-matching of the digitally controlled system are formulated in terms of linear matrix inequalities (LMIs). Finally, a TS fuzzy model for the chaotic Lorentz system is used as an . example to guarantee the stability and effectiveness of the proposed method.

• Journal of Radiation Protection and Research
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• v.17 no.1
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• pp.43-56
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• 1992

As one of the methods to ameliorate the ray effects which are the nature of anomalous computational effects due to the discretization of the angular variable in discrete ordinates approximations, a computational program, named TWODET (TWO dimensional Discrete Element Transport), has developed in 2 dimensional cartesian coordinates system using the discrete elements method, in which the discrete angle quadratures are steered by the spatially dependent angular fluxes. The results of the TWODET calculation with K-2, L-3 discrete angular quadratures, in the problem of a centrally located, isotropically emitting flat source in an absorbing square, are shown to be more accurate than that of the DOT 4.3 calculation with S-10 full symmetry angular quadratures, in remedy of the ray effect at the edge flux distributions of the square. But the computing time of the TWODET is about 4 times more than that of the DOT 4.3. In the problem of vacuum boundaries just outside of the source region in an absorbing square, the results of the TWODET calculation are shown severely anomalous ray effects, due to the sudden discontinuity between the source and the vacuum, like as the results of the DOT 4.3 calculation. In the probelm of an external source in an absorbing square in which a highly absorbing medium is added, the results of the TWODET calculation with K-3, L-4 show a good ones like as, somewhat more than, that of the DOT 4.3 calculation with S-10.

• Computers and Concrete
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• v.16 no.5
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• pp.669-682
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• 2015

Degradation of reinforced concrete (RC) structures due to chloride penetration followed by reinforcement corrosion has been a serious problem in civil engineering for many years. The numerical simulation methods at present are mainly finite element method (FEM) and finite difference method (FDM), which are based on mesh. Mesh generation in engineering takes a long time. In the present article, the numerical solution of chloride transport in concrete is analyzed using radial point interpolation method (RPIM) and element-free Galerkin (EFG). They are all meshless methods. RPIM utilizes radial polynomial basis, whereas EFG uses the moving least-square approximation. A Galerkin weak form on global is used to attain the discrete equation, and four different numerical examples are presented. MQ function and appropriate parameters have been proposed in RPIM. Numerical simulation results are compared with those obtained from the finite element method (FEM) and analytical solutions. Two case of chloride transport in full saturated and unsaturated concrete are analyzed to test the practical applicability and performance of the RPIM and EFG. A good agreement is obtained among RPIM, EFG, and the experimental data. It indicates that RPIM and EFG are reliable meshless methods for prediction of chloride concentration in concrete structures.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.51 no.11
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• pp.551-558
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• 2002

A time-domain combined field integral equation (CFIE) is presented to obtain the transient scattering response from arbitrarily shaped three-dimensional conducting bodies. This formulation is based on a linear combination of the time-domain electric field integral equation (EFIE) with the magnetic field integral equation (MFIE). The time derivative of the magnetic vector potential in EFIE is approximated using a central finite difference approximation and the scalar potential is averaged over time. The time-domain CFIE approach produces results that are accurate and stable when solving for transient scattering responses from conducting objects. The incident spectrum of the field may contain frequency components, which correspond to the internal resonance of the structure. For the numerical solution, we consider both the explicit and implicit scheme and use two different kinds of Gaussian pulses, which may contain frequencies corresponding to the internal resonance. Numerical results for the EFIE, MFIE, and CFIE are presented and compared with those obtained from the inverse discrete Fourier transform (IDFT) of the frequency-domain CFIE solution.

• Communications for Statistical Applications and Methods
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• v.20 no.6
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• pp.439-454
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• 2013

This study presents a Bayesian multiple change-point detection approach to segment and classify the observations that no longer come from an initial population after a certain time. Inferences are based on the multiple change-points in a sequence of random variables where the probability distribution changes. Bayesian multiple change-point estimation is classifies each observation into a segment. We use a truncated Poisson distribution for the number of change-points and conjugate prior for the exponential family distributions. The Bayesian method can lead the unsupervised classification of discrete, continuous variables and multivariate vectors based on latent class models; therefore, the solution for change-points corresponds to the stochastic partitions of observed data. We demonstrate segmentation with real data.

• Coupled systems mechanics
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• v.11 no.2
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• pp.167-198
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• 2022

In this paper we deal with classical instability problems of heterogeneous Euler beam under conservative loading. It is chosen as the model problem to systematically present several possible solution methods from simplest deterministic to more complex stochastic approach, both of which that can handle more complex engineering problems. We first present classical analytic solution along with rigorous definition of the classical Euler buckling problem starting from homogeneous beam with either simplified linearized theory or the most general geometrically exact beam theory. We then present the numerical solution to this problem by using reduced model constructed by discrete approximation based upon the weak form of the instability problem featuring von Karman (virtual) strain combined with the finite element method. We explain how such numerical approach can easily be adapted to solving instability problems much more complex than classical Euler's beam and in particular for heterogeneous beam, where analytic solution is not readily available. We finally present the stochastic approach making use of the Duffing oscillator, as the corresponding reduced model for heterogeneous Euler's beam within the dynamics framework. We show that such an approach allows computing probability density function quantifying all possible solutions to this instability problem. We conclude that increased computational cost of the stochastic framework is more than compensated by its ability to take into account beam material heterogeneities described in terms of fast oscillating stochastic process, which is typical of time evolution of internal variables describing plasticity and damage.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.4
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• pp.493-499
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• 2007

The Taylor expansion expresses a differentiable function and its coefficients provide good approximations for the given function and its derivatives. In this study, m-th order Taylor Polynomial is constructed and the coefficients are computed by the Moving Least Squares method. The coefficients are applied to the governing partial differential equation for solid problems including crack problems. The discrete system of difference equations are set up based on the concept of point collocation. The developed method effectively overcomes the shortcomings of the finite difference method which is dependent of the grid structure and has no approximation function, and the Galerkin-based meshfree method which involves time-consuming integration of weak form and differentiation of the shape function and cumbersome treatment of essential boundary.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.3
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• pp.285-290
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• 2007

In this paper, we presents robust digital redesign (DR) method for observer-based linear time-invariant (LTI) system. The term of DR involves converting an analog controller into an equivalent digital one by considering two condition: state-matching and stability. The design problems viewed as a convex optimization problem that we minimize the error of the norm bounds between interpolated linear operators to be matched. Also, by using the bilinear and inverse bilinear approximation method, we analyzed the uncertain parts of given observer-based system more precisely, When a sampling period is sufficiently small, the conversion of a analog structured uncertain system to an equivalent discrete-time system have proper reason. Sufficiently conditions for the state-matching of the digitally controlled system are formulated in terms of linear matrix inequalities (LMIs).

• Journal of the Korean institute of surface engineering
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• v.53 no.3
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• pp.95-103
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• 2020

In this study, the material used in the hot dip galvanizing equipment was poorly corrosion-resistant, so it was performed to solve the cost and time problems caused by equipment replacement. The theoretical calculation was performed using the DV-Xα method(Discrete Variational Local-density approximation method). The alloy (STS4XX series) of the equipment currently used has a martensite phase. Therefore, the theoretical calculation was performed by applying P4 / mmm, which is a tetragonal structure. The new alloy was chosen by designing theoretical values close to existing materials. Considering elements that contribute to corrosion, most have high prices. Therefore, the design was completed by adjusting the content using only the components of the reference material in the theoretical design. The final design alloys were chosen as D6 and D9. Designed D6 and D9 were dissolved and prepared using an induction furnace. After the heat treatment process was completed, the corrosion rate of the alloys was confirmed by using the potentiodynamic polarization test. The surface of the prepared alloys were processed horizontally and then polished to # 1200 using sand paper to perform potentiodynamic polarization test. Domestic products: 4.735 mpy (mils / year), D6: 0.9166 mpy, D9: 0.3372 mpy, alloys designed than domestic products had a lower corrosion rate. Therefore, the designed alloy was expected to have better erosion resistance.