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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
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Journal of the Korea Society for Industrial and Applied Mathematics
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Journal DOI :
The Korean Society for Industrial and Applied Mathematics
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Volume & Issues
Volume 18, Issue 4 - Dec 2014
Volume 18, Issue 3 - Sep 2014
Volume 18, Issue 2 - Jun 2014
Volume 18, Issue 1 - Mar 2014
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OPTIMAL STRATEGIES FOR PREVENTION OF ECSTASY USE
Choi, Sunhwa ; Lee, Jonggul ; Jung, Eunok ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 18, issue 1, 2014, Pages 1~15
DOI : 10.12941/jksiam.2014.18.001
We have investigated optimal control strategies for prevention of ecstasy use. Ecstasy use has continued at raves and nightclubs in recent years and the reduction of ecstasy use has become one of the important issues in society. We apply optimal control theory to a model of the peer-driven dynamics of ecstasy use. Our goal is to minimize the ecstasy use class and the intervention cost. Optimal control is characterized in terms of the solution of optimality system, which is the state system coupled with the adjoint system and the optimality equations. The numerical simulations show the optimal prevention policies of ecstasy use in various scenarios.
ADVANCED DOMAIN DECOMPOSITION METHOD BY LOCAL AND MIXED LAGRANGE MULTIPLIERS
Kwak, Junyoung ; Chun, Taeyoung ; Cho, Haeseong ; Shin, Sangjoon ; Bauchau, Olivier A. ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 18, issue 1, 2014, Pages 17~26
DOI : 10.12941/jksiam.2014.18.017
This paper presents development of an improved domain decomposition method for large scale structural problem that aims to provide high computational efficiency. In the previous researches, we developed the domain decomposition algorithm based on augmented Lagrangian formulation and proved numerical efficiency under both serial and parallel computing environment. In this paper, new computational analysis by the proposed domain decomposition method is performed. For this purpose, reduction in computational time achieved by the proposed algorithm is compared with that obtained by the dual-primal FETI method under serial computing condition. It is found that the proposed methods significantly accelerate the computational speed for a linear structural problem.
A NUMERICAL METHOD FOR THE MODIFIED VECTOR-VALUED ALLEN-CAHN PHASE-FIELD MODEL AND ITS APPLICATION TO MULTIPHASE IMAGE SEGMENTATION
Lee, Hyun Geun ; Lee, June-Yub ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 18, issue 1, 2014, Pages 27~41
DOI : 10.12941/jksiam.2014.18.027
In this paper, we present an efficient numerical method for multiphase image segmentation using a multiphase-field model. The method combines the vector-valued Allen-Cahn phase-field equation with initial data fitting terms containing prescribed interface width and fidelity constants. An efficient numerical solution is achieved using the recently developed hybrid operator splitting method for the vector-valued Allen-Cahn phase-field equation. We split the modified vector-valued Allen-Cahn equation into a nonlinear equation and a linear diffusion equation with a source term. The linear diffusion equation is discretized using an implicit scheme and the resulting implicit discrete system of equations is solved by a multigrid method. The nonlinear equation is solved semi-analytically using a closed-form solution. And by treating the source term of the linear diffusion equation explicitly, we solve the modified vector-valued Allen-Cahn equation in a decoupled way. By decoupling the governing equation, we can speed up the segmentation process with multiple phases. We perform some characteristic numerical experiments for multiphase image segmentation.
EULER-MARUYAMA METHOD FOR SOME NONLINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH JUMP-DIFFUSION
Ahmed, Hamdy M. ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 18, issue 1, 2014, Pages 43~50
DOI : 10.12941/jksiam.2014.18.043
In this paper we discussed Euler-Maruyama method for stochastic differential equations with jump diffusion. We give a convergence result for Euler-Maruyama where the coefficients of the stochastic differential equation are locally Lipschitz and the pth moments of the exact and numerical solution are bounded for some p > 2.
A REVIEW OF THE SUPRA-CONVERGENCES OF SHORTLEY-WELLER METHOD FOR POISSON EQUATION
Yoon, Gangjoon ; Min, Chohong ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 18, issue 1, 2014, Pages 51~60
DOI : 10.12941/jksiam.2014.18.051
The Shortley-Weller method is a basic finite difference method for solving the Poisson equation with Dirichlet boundary condition. In this article, we review the analysis for supra-convergence of the Shortley-Weller method. Though consistency error is first order accurate at some locations, the convergence order is globally second order. We call this increase of the order of accuracy, supra-convergence. Our review is not a simple copy but serves a basic foundation to go toward yet undiscovered analysis for another supra-convergence: we present a partial result for supra-convergence for the gradient of solution.
ACCURATE AND EFFICIENT COMPUTATIONS FOR THE GREEKS OF EUROPEAN MULTI-ASSET OPTIONS
Lee, Seunggyu ; Li, Yibao ; Choi, Yongho ; Hwang, Hyoungseok ; Kim, Junseok ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 18, issue 1, 2014, Pages 61~74
DOI : 10.12941/jksiam.2014.18.061
This paper presents accurate and efficient numerical methods for calculating the sensitivities of two-asset European options, the Greeks. The Greeks are important financial instruments in management of economic value at risk due to changing market conditions. The option pricing model is based on the Black-Scholes partial differential equation. The model is discretized by using a finite difference method and resulting discrete equations are solved by means of an operator splitting method. For Delta, Gamma, and Theta, we investigate the effect of high-order discretizations. For Rho and Vega, we develop an accurate and robust automatic algorithm for finding an optimal value. A cash-or-nothing option is taken to demonstrate the performance of the proposed algorithm for calculating the Greeks. The results show that the new treatment gives automatic and robust calculations for the Greeks.