• Steel and Composite Structures
• /
• v.20 no.5
• /
• pp.1087-1102
• /
• 2016

The paper proposes to characterize the free vibration behaviour of non-uniform cylindrical shells using spline approximation under first order shear deformation theory. The system of coupled differential equations in terms of displacement and rotational functions are obtained. These functions are approximated by cubic splines. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector which are spline coefficients. Four and two layered cylindrical shells consisting of two different lamination materials and plies comprising of same as well as different materials under two different boundary conditions are analyzed. The effect of length parameter, circumferential node number, material properties, ply orientation, number of lay ups, and coefficients of thickness variations on the frequency parameter is investigated.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.16 no.1
• /
• pp.15-29
• /
• 2012

In this paper we introduce 6-fold symmetry crystal growth using new phase-field models based on the modified Allen-Cahn equation. The proposed method is a hybrid method which uses both analytic and numerical solutions. We then show this method can be extended to $k$-fold case. The Wulff construction procedure is provided to understand and predict the shape of crystals. We also present a detailed mathematical proof of the validity of the Wulff construction. For computational results, we verify the accuracy and efficiency of the method for snow crystal growth.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.22 no.1
• /
• pp.1-13
• /
• 2018

Boosting, one of the most successful algorithms for supervised learning, searches the most accurate weighted sum of weak classifiers. The search corresponds to a convex programming with non-negativity and affine constraint. In this article, we propose a novel Conjugate Gradient algorithm with the Modified Polak-Ribiera-Polyak conjugate direction. The convergence of the algorithm is proved and we report its successful applications to boosting.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.17 no.4
• /
• pp.295-306
• /
• 2013

In this paper, we consider the adaptive multigrid method for solving the Black-Scholes equation to improve the efficiency of the option pricing. Adaptive meshing is generally regarded as an indispensable tool because of reduction of the computational costs. The Black-Scholes equation is discretized using a Crank-Nicolson scheme on block-structured adaptively refined rectangular meshes. And the resulting discrete equations are solved by a fast solver such as a multigrid method. Numerical simulations are performed to confirm the efficiency of the adaptive multigrid technique. In particular, through the comparison of computational results on adaptively refined mesh and uniform mesh, we show that adaptively refined mesh solver is superior to a standard method.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.25 no.3
• /
• pp.82-92
• /
• 2021

In this study, we present a fast option pricing method for four asset equity-linked securities (ELS) using Brownian bridge. The proposed method is based on Monte Carlo simulation (MCS) and a Brownian bridge approach. Currently, three asset ELS is the most popular ELS among multi-asset ELSs. However, four asset ELS emerged as an alternative to three asset ELS under low interest rate environment to give higher coupon rate to investors. We describe in detail the computational solution algorithm for the four underlying asset step-down ELS. The numerical tests confirm the accuracy and speed of the method.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.27 no.2
• /
• pp.87-108
• /
• 2023

This is a review paper on recent development on the spectral theory of the Neumann-Poincaré operator. The topics to be covered are convergence rate of eigenvalues of the Neumann-Poincaré operator and surface localization of the single layer potentials of its eigenfunctions. Study on these topics is motivated by their relations with the cloaking by anomalous localized resonance. We review on this topic as well.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.26 no.1
• /
• pp.1-22
• /
• 2022

A tandem queue that consists of nodes with buffers of finite capacity and general blocking scheme is considered. The service time distribution of each node is exponential whose rate depends on the state of the node. The blocking scheme at a node may be different from that of other nodes. An approximation method for the system based on decomposition method is presented. The effectiveness of the method is investigated numerically.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.27 no.4
• /
• pp.281-295
• /
• 2023

This study aims to establish and analyze a mathematical model for the transmission dynamics of male adolescent smoking and to determine an optimal control strategy to reduce male adolescent smoking. We consider three groups in the population: smokers, non-smokers, and temporary nonsmokers. In our model to which optimal control theory was applied, the number of smokers decreased sharply and the number of non-smokers increased significantly. Our simulation results under various control scenarios reveal that integrated control measures(such as prevention, education, and treatment) may be necessary to reduce the growth rate of adolescent smoking. Moreover, we concluded that efforts to encourage current smokers and temporary quitters to quit should be sustained longer than efforts to reduce the rate at which nonsmokers become smokers through smoking prevention education.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.20 no.1
• /
• pp.83-106
• /
• 2016

This paper reviews and compares three different methods for modeling incompressible and immiscible ternary fluid flows: the immersed boundary, level set, and phase-field methods. The immersed boundary method represents the moving interface by tracking the Lagrangian particles. In the level set method, an interface is defined implicitly by using the signed distance function, and its evolution is governed by a transport equation. In the phase-field method, the advective Cahn-Hilliard equation is used as the evolution equation, and its order parameter also implicitly defines an interface. Each method has its merits and demerits. We perform the several simulations under different conditions to examine the merits and demerits of each method. Based on the results, we determine the most suitable method depending on the specific modeling needs of different situations.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.19 no.2
• /
• pp.103-121
• /
• 2015

In this paper, we briefly review and describe a projection algorithm for numerically computing the two-dimensional time-dependent incompressible Navier-Stokes equation. The projection method, which was originally introduced by Alexandre Chorin [A.J. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comput., 22 (1968), pp. 745-762], is an effective numerical method for solving time-dependent incompressible fluid flow problems. The key advantage of the projection method is that we do not compute the momentum and the continuity equations at the same time, which is computationally difficult and costly. In the projection method, we compute an intermediate velocity vector field that is then projected onto divergence-free fields to recover the divergence-free velocity. Numerical solutions for flows inside a driven cavity are presented. We also provide the source code for the programs so that interested readers can modify the programs and adapt them for their own purposes.