• The Transactions of the Korea Information Processing Society
• /
• v.2 no.6
• /
• pp.960-968
• /
• 1995

In this paper we present a reordering scheme that could lead to efficient vectorization of the preconditioners for the large sparse linear systems arising from partial differential equations on the CRAY-2, This reordering scheme is a line version of the conventional red/black ordering. This reordering scheme, coupled with a variant of ILU(Incomplete LU) preconditioning, can overcome the poor rate of convergence of the conventional red/black reordering, if relatively large number of fill-ins were used. We substantiate our claim by conducting various experiments on the CRAY-2 machine. Also, the computation of the Frobenius norm of the error matrices agree with our claim.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.14 no.3
• /
• pp.175-187
• /
• 2010

This paper presents the numerical valuation of the two-asset step-down equitylinked securities (ELS) option by using the operator-splitting method (OSM). The ELS is one of the most popular financial options. The value of ELS option can be modeled by a modified Black-Scholes partial differential equation. However, regardless of whether there is a closedform solution, it is difficult and not efficient to evaluate the solution because such a solution would be represented by multiple integrations. Thus, a fast and accurate numerical algorithm is needed to value the price of the ELS option. This paper uses a finite difference method to discretize the governing equation and applies the OSM to solve the resulting discrete equations. The OSM is very robust and accurate in evaluating finite difference discretizations. We provide a detailed numerical algorithm and computational results showing the performance of the method for two underlying asset option pricing problems such as cash-or-nothing and stepdown ELS. Final option value of two-asset step-down ELS is obtained by a weighted average value using probability which is estimated by performing a MC simulation.

• Water for future
• /
• v.15 no.1
• /
• pp.57-62
• /
• 1982

In order to make a numerical modeling for the one dimensional unsteady flow which expressed by Saint Venant partial differential equations, Preissman's implicit schem was used, and it's stability and accuracy was investigated. By introducing recurrence relations make it possible to use double sweep algorithm. Effective parameters to the result were the values of the C$$ and the Chezy coefticient. In order to get numerical solutions whith enough accuracy, C$$ should not be far from the value of1, and when the criteria of the $\theta$ was 0.6<$\theta$<1.0, the rewult was always stable for any condition. This model should be calibrated by real field data, and expected to be developed for the simulation of the river system and to the long wave analysis for one dimensional coastal zone problem.

• Journal of the Korean Society for Precision Engineering
• /
• v.23 no.6 s.183
• /
• pp.119-127
• /
• 2006

A non-destructive time domain approach to examine structural damage using parameterized partial differential equations and Galerkin approximation techniques is presented. The time domain analysis for damage detection is independent of modal parameters and analytical models unlike frequency domain methods which generally rely on analytical models. The time history of the vibration response of the structure was used to identify the presence of damage. Damage in a structure causes changes in the physical coefficients of mass density, elastic modulus and damping coefficients. This is a part of our ongoing effort on the general problem of modeling and parameter estimation for internal damping mechanisms in a composite beam. Namely, in detecting damage through time-domain or frequency-domain data from smart sensors, the common damages are changed in modal properties such as natural frequencies, mode shapes, and mode shape curvature. This paper examines the use of beam-like structures with piezoceramic sensors and actuators to perform identification of those physical parameters, and detect the damage. Experimental results are presented from tests on cantilevered composite beams damaged at different locations and different dimensions. It is demonstrated that the method can sense the presence of damage and obtain the position of a damage.

• Journal of Biosystems Engineering
• /
• v.22 no.3
• /
• pp.279-288
• /
• 1997

This study was worked out to obtain fundamental data needed for developing a continuous type dryer. The drying process in a cross-flow type continuous dryer was expressed as partial differential equations, and a drying simulation model for predicting rice moisture content, rice temperature, drying air absolute humidity, drying air temperature was developed by using the finite difference method. To validate the performance of the drying simulation model, a prototype continuous dryer was constructed in this study. The size of the test dryer was one-tenth to that of a commercial continuous dryer. The difference in the outlet rice moisture content between the predicted values and the measured values was within 0.5%, that of outlet rice temperature was below $3^{\circ}C$, that of drying air temperature in drying bed was within $8^{\circ}C$ and that of relative humidity of outlet drying air was big because of the different measuring point. In addition, a drying simulation model for a actual size continuous dryer with double flow was developed in this study. This drying simulation model included the rice mixing effect in the middle of drying length. The difference of outlet moisture content between the predicted and the measured values showed below 0.5% in this study.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.14 no.3
• /
• pp.453-462
• /
• 1994

Variation of seismic wave field in a multi-layered attenuating elastic half space is studied by the propagator matrix method and point source models of which fault-slip functions are defined as ramp functions. In this paper, the earth is modeled as being composed of horizontally stratified layers, with uniform material properties for each layer. The partial differential equations for the seismic motion in each layer are solved using a Fourier Hankel transform approach. Time histories and frequency contents of accelerations and displacements due to a vertical dip-slip and strike-slip point source located in the underlain half space are calculated at the layer interfaces using the developed programs and their characteristics are represented.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.19 no.1
• /
• pp.1-21
• /
• 2015

This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.

• Structural Engineering and Mechanics
• /
• v.62 no.6
• /
• pp.759-769
• /
• 2017

The effect of central axial load on natural frequencies of various thin-walled beams, are investigated by some researchers using different methods such as finite element, transfer matrix and dynamic stiffness matrix methods. However, there are situations that the load will be off centre. This type of loading is called eccentric load. The effect of the eccentricity of axial load on the natural frequencies of asymmetric thin-walled beams is a subject that has not been investigated so far. In this paper, the mentioned effect is studied using exact dynamic stiffness matrix method. Flexure and torsion of the aforesaid thin-walled beam is based on the Bernoulli-Euler and Vlasov theories, respectively. Therefore, the intended thin-walled beam has flexural rigidity, saint-venant torsional rigidity and warping rigidity. In this paper, the Hamilton‟s principle is used for deriving governing partial differential equations of motion and force boundary conditions. Throughout the process, the uniform distribution of mass in the member is accounted for exactly and thus necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, in order to verify the accuracy of the presented theory, the numerical solutions are given and compared with the results that are available in the literature and finite element solutions using ABAQUS software.

• Journal of the Korean Solar Energy Society
• /
• v.23 no.1
• /
• pp.29-38
• /
• 2003

To develope chemical heat pump using available energy sources, solar heat and other kinds of waste thermal energy, we have studied the material and heat transfer rate in the cylindrical bed reactor packed with Calcined Dolomite. Our results from the studies are as follows ; 1 The time needed to complete dehydration reaction at the wall side of the cylindrical reactor(r/rL=0.5) was shorter than that of the center(r/rL=0.0) as much as 12%. 2. Two dimensional (radial and circumferential) partial differential equations, concerning heat and mass transfer rate in the packed bed of calcined Dolomite, are solved numerically to describe the characteristics of the reaction in the cylindrical reactor. The solution reads rate of reaction in the packed bed reactor depends on the temperature and concentration of reactants. These results read the supplied heat transfers from the wall side of the cylinder to the center, dehydration reaction begins at the inner side of the wall of the cylindrical reactor and the dehydration reaction proceeds from the wall side to center of cylinder.

• Journal of the Institute of Electronics Engineers of Korea CI
• /
• v.42 no.1
• /
• pp.79-87
• /
• 2005

This paper presents an active contour model for extracting accurate facial regions in complex environments. In the model, a contour is represented by a zero level set of level function φ, and evolved via level set partial differential equations. Then, unlike general active contours, skin color information that is represented by 2D Gaussian model is used for evolving and slopping a curve, which allows the proposed method to be robust to noise and varying pose. To assess the effectiveness of the proposed method it was tested with several natural scenes, and the results were compared with those of geodesic active contours. Experimental results demonstrate the superior performance of the proposed method.