• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.193-213
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• 2017

We investigate an efficient approximation of solution to stochastic Burgers equation driven by an additive space-time noise. We discuss existence and uniqueness of a solution through the Orstein-Uhlenbeck (OU) process. To approximate the OU process, we introduce the Karhunen-$Lo{\grave{e}}ve$ expansion, and sparse grid stochastic collocation method. About spatial discretization of Burgers equation, two separate finite element approximations are presented: the conventional Galerkin method and Galerkin-conservation method. Numerical experiments are provided to demonstrate the efficacy of schemes mentioned above.

• East Asian mathematical journal
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• v.24 no.1
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• pp.81-95
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• 2008

Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T\;:\;C\;{\rightarrow}\;E$ a nonexpansive mapping satisfying the weak inwardness condition. Assume that every weakly compact convex subset of E has the fixed point property. For $f\;:\;C\;{\rightarrow}\;C$ a contraction and $t\;{\in}\;(0,\;1)$, let $x_t$ be a unique fixed point of a contraction $T_t\;:\;C\;{\rightarrow}\;E$, defined by $T_tx\;=\;tf(x)\;+\;(1\;-\;t)Tx$, $x\;{\in}\;C$. It is proved that if {$x_t$} is bounded, then $x_t$ converges to a fixed point of T, which is the unique solution of certain variational inequality. Moreover, the strong convergence of other implicit and explicit iterative schemes involving the sunny nonexpansive retraction is also given in a reflexive and strictly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.156-157
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• 2003

A simple method is proposed to split the flux vector of the Euler equations by introducing two artificial wave speeds. The direction of wave propagation can be adjusted by these two wave speeds. This idea greatly simplifies the upwinding, and leads to a new family of upwind schemes. Numerical flux function for multi-dimensional Euler equations is formulated for any grid system, structured or unstructured. A remarkable simplicity of the scheme is that it successfully achieves one-sided approximation for all waves without recourse to any matrix operation. Moreover, its accuracy is comparable with the exact Riemann solver. For 1-D Euler equations, the scheme actually surpasses the exact solver in avoiding expansion shocks without any additional entropy fix. The scheme can exactly resolve stationary contact discontinuities, and it is also freed of the carbuncle problem in multi­dimensional computations.

• Korean Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.140-144
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• 1998

We propose the area between a pair of non-self-intersecting 2-D parametric curves with same endpoints as an alternative distance metric between the curves. This metric is used when d curve is approximated with another in a simpler form to evaluate how good the approximation is. The traditional set-theoretic Hausdorff distance can he defined for any pair of curves but requires expensive calculations. Our proposed metric is not only intuitively appealing but also very easy to numerically compute. We present the numerical schemes and test it on some examples to show that our proposed metric converges in a few steps within a high accuracy.

• International Journal of Internet, Broadcasting and Communication
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• v.9 no.1
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• pp.72-80
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• 2017

In this work, an efficient transmit antenna selection approach for the quadrature spatial modulation (QSM) systems is proposed. The conventional Euclidean distance antenna selection (EDAS)-based schemes in QSM have too high computational complexity for practical use. The proposed antenna selection algorithm is based on approximation of the EDAS decision metric employed for QSM. The elimination of imaginary parts in the decision metric enables decoupling of the approximated decision metric, which enormously reduces the complexity. The proposed method is also evaluated via simulations in terms of symbol error rate (SER) performance and compared with the conventional EDAS methods in QSM systems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.4
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• pp.238-266
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• 2013

The Interaction Picture (IP) method is a valuable alternative to Split-step methods for solving certain types of partial differential equations such as the nonlinear Schr$\ddot{o}$dinger equation or the Gross-Pitaevskii equation. Although very similar to the Symmetric Split-step (SS) method in its inner computational structure, the IP method results from a change of unknown and therefore do not involve approximation such as the one resulting from the use of a splitting formula. In its standard form the IP method such as the SS method is used in conjunction with the classical 4th order Runge-Kutta (RK) scheme. However it appears to be relevant to look for RK scheme of higher order so as to improve the accuracy of the IP method. In this paper we investigate 5th order Embedded Runge-Kutta schemes suited to be used in conjunction with the IP method and designed to deliver a local error estimation for adaptive step size control.

• 전기의세계
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• v.22 no.3
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• pp.49-62
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• 1973

An algorithm for the state estimation and identification of multivariable nonlinear systems with noisy nonlinear observation has been investigated on the basis of the multidimensional Hermitian expansion for the a posteriori probability densities of the predicted observation, the predicted state and the observation conditioned by the state. A new approach for construction of this sequential nonlinear estimator, retaining up to the second order term of the observation error, has been developed, along with the approximation of nonlinear system functions, truncating at the second term. The estimation of the unknown parameters has been established by extending the state estimation technique, regarding the parameters as another state variables. The results of investigation indicate the feasibility of the schemes presented in this paper.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.13 no.2
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• pp.81-87
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• 2004

This paper deals with a new approach to tolerance optimization problems. Optimal tolerance allotment problems can be formulated as stochastic optimization problems. Most schemes to solve the stochastic optimization problems have been found to exhibit difficulties in multivariate integration of the probability density function. As a typical example of stochastic optimization the optimal tolerance allotment problem has the same difficulties. In this stochastic model, manufacturing system is represented by Gauss-Markov stochastic process and the manufacturing unit availability is characterized for realistic optimization modeling. The new algorithm performed robustly for a large deviation approximation. A significant reduction in computation time was observed compared to the results obtained in previous studies.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.7
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• pp.1411-1418
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• 1997

This paper presents a statistical analysis of the decision throeshold for derect-sequence spread-spectrum (DS-SS) prallel Pseudo-Noise (PN) code acquistion with a reference filter. The probabilities of detection and false alarm are derived, and the mean acquistion time is evaluated as a measure of the system performance in both nonfading and Rician fiding channels. From the statistical sresults, it is shown that in the performance analysis of the parallel acquisition system with reference filtering, the statistical evaluaion of the decision threshold seems more appropriate than the approximation of the decision threshold adopted in the other schemes[2,3].

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1996.10a
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• pp.158-161
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• 1996

A robust adaptive tracking control architecture is proposed for a class of continuous-time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible. The architecture employs an adaptive fuzzy system to compensate for the uncertainty of the plant. In order to improve the robustness under approximation errors and disturbances, the proposed architecture includes deadzone in adaptation laws. Unlike the previously proposed schemes, the magnitude of approximate errors and disturbances is not required in the determination of the deadzone size, since it is estimated using the adaptation law. The proposed algorithm is proven to be globally stable in the Lyapunov sense, with tracking errors converging to the proposed architecture.