• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.231-249
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• 2020

We present an efficient and robust finite difference method for a two-asset jump diffusion model, which is a partial integro-differential equation (PIDE). To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. In addition, we use bilinear interpolation to solve integral term of PIDE. We can obtain more stable value by using the payoff-consistent extrapolation. We provide numerical experiments to demonstrate a performance of the proposed numerical method. The numerical results show the robustness and accuracy of the proposed method.

• IEMEK Journal of Embedded Systems and Applications
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• v.9 no.6
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• pp.335-344
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• 2014

As a kind of 2D spatial coordinate transform, image warping is a basic image processing technique utilized in various applications. Though image warping algorithm is composed of relatively simple operations such as memory accesses and computations of weighted average, real-time implementations on embedded vision systems suffer from limited computational power because the simple operations are iterated as many times as the number of pixels. This paper presents a real-time implementation of a look-up table(LUT)-based image warping using an FPGA. In order to ensure sufficient data transfer rate from memories storing mapping LUT and image data, appropriate memory devices are selected by analyzing memory access patterns in an LUT-based image warping using backward mapping. In addition, hardware structure of a parallel and pipelined architecture is proposed for fast computation of bilinear interpolation using fixed-point operations. Accuracy of the implemented hardware is verified using a synthesized test image, and an application to real-time lens distortion correction is exemplified.

• International Journal of Naval Architecture and Ocean Engineering
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• v.10 no.3
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• pp.329-347
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• 2018

The Smoothed Particle Hydrodynamics (SPH) method has proved to have great potentials in dealing with the wave-structure interactions. Compared with the Weakly Compressible SPH (WCSPH) method, the ISPH approach solves the pressure by using the pressure Poisson equation rather than the equation of state. This could provide a more stable and accurate pressure field that is important in the study of wave-structure interactions. This paper improves the solid boundary treatment of ISPH by using a high accuracy Simplified Finite Difference Interpolation (SFDI) scheme for the 2D wave-structure coupling problems, especially for free-moving structure. The proposed method is referred as the ISPH_BS. The model improvement is demonstrated by the documented benchmark tests and laboratory experiment covering various wave-structure interaction applications.

• Wind and Structures
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• v.27 no.4
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• pp.235-245
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• 2018

In this study the stress analysis of orthotropic thin plate with arbitrary shapes for different boundary conditionsis investigated. Meshfreemethod is applied to static analysis of thin plates with various geometries based on the Kirchhoff classical plate theory. According to the meshfree method the domain of the plates are expressed through a set of nodes without using mesh. In this method, a set of nodes are defined in a standard rectangular domain, then via a third order map, these nodes are transferred to the main domain of the original geometry; therefore the analysis of the plates can be done. Herein, Meshless local Petrov-Galerkin (MLPG) as a meshfree numerical method is utilized. The MLS function in MLPG does not satisfy essential boundary conditions using Delta Kronecker. In the MLPG method, direct interpolation of the boundary conditions can be applied due to constructing node by node of the system equations. The detailed parametric study is conducted, focusing on the arbitrary geometries of the thin plates. Results show that the meshfree method provides better accuracy rather than finite element method. Also, it is found that trend of the figures have good agreement with relevant published papers.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.748-753
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• 2001

The objective of the present study is to visualize the pulsatile flow fields by using three-dimensional computer simulation and the PIV system. A closed flow loop system was built for the steady and unsteady experiments. The Harvard pulsatile pump was used to generate the pulsatile pressure and velocity waveforms. Conifer powder as the tracing particles was added to water to visualize the flow field. Two consecutive particle images were captured by a CCO camera for the image processing at several cross section. The range validation and the area interpolation methods were used to obtain the final velocity vectors with high accuracy. The finite volume predictions were used to analyze three-dimensional flow patterns in the bifurcation model. The results of the PIV experiment and the computer simulation are in good agreement and the results show the recirculation zones and formation of the paired secondary flow distal to the apex of the bifurcated model. The results also show that the branch flow is pushed strongly to the inner wall due to the inertial force effect and helical motions are generated as the flow proceeds toward the outer wall.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.6
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• pp.619-627
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• 2004

In most industrial applications, the geometrical complexity is combined with the moving boundaries. These problems considerably increase the computational difficulties since they require, respectively, regeneration and deformation of the grid. As a result, engineering flow simulation is restricted. In order to solve this kind of problems the immersed boundary method was developed. In this study, the immersed boundary method is applied to the numerical simulation of stationary, rotating and oscillating cylinders in the 2-dimensional square cavity. No-slip velocity boundary conditions are given by imposing feedback forcing term to the momentum equation. Besides, this technique is used with a second-order accurate interpolation scheme in order to improve the accuracy of flow near the immersed boundaries. The governing equations for the mass and momentum using the immersed boundary method are discretized on the non-staggered grid by using the finite volume method. The results agree well with previous numerical and experimental results. This study presents the possibility of the immersed boundary method to apply to the complex flow experienced in the industrial applications. The usefulness of this method will be confirmed when we solve the complex geometries and moving bodies.

• Journal of the Korea Computer Graphics Society
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• v.15 no.1
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• pp.1-6
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• 2009

This paper presents a new CIP method for unstructured mesh to reduce the numerical dissipation. To reflect precise physical characteristics, CIP method updates both the physical quantity and the derivative information. The proposed method uses the Finite Volume Method(FVM) to solve the non-advection term of CIP equation. And we performed several experiments to improve the accuracy of third-order interpolation. Our result shows that our algorithm has less numerical dissipation than that of linear advection solver.

• Journal of computational fluids engineering
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• v.20 no.3
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• pp.20-26
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• 2015

This paper introduces a computational method for analysis of the 6-DOF motions of a ship in waves using an overset grid technique which consists of inner and outer domains for representing body motions and numerical wave tank, respectively. High order interpolation scheme is employed to increase numerical accuracy over the interface where physical values, such as velocities and pressure, interact between the inner and outer domains. The numerical schemes and algorithm are addressed in the present paper. An application to motion of KCS container carrier in head waves is presented, and the comparison of responses on heave and pitch motions shows good agreement with those of model tests.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.602-606
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• 2005

A systematic procedure of probability analysis for general distributions is developed based on the first four moments estimated from polynomial interpolation of the system response function and the Pearson system. The function approximation is based on a specially selected experimental region for accuracy and the number of function evaluations is taken equal to that of the unknown coefficient for efficiency. For this purpose, three error-minimizing conditions are proposed and corresponding canonical experimental regions are formed for popular probability. This approach is applied to study the stochastic properties of the performance functions of a MEMS structure, which has quite large fabrication errors compared to other structures. Especially, the vibratory micro-gyroscope is studied using the statistical moments and probability density function (PDF) of the performance function to be the difference between resonant frequencies corresponding to sensing and driving mode. The results show that it is very sensitive to the fabrication errors and that the types of PDF of each variable also affect the stochastic properties of the performance function although they have same the mean and variance.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.100-103
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• 2005

In this study, tool path control algorithm for aspherical surface grinding was derived and discussed. The aspherical surface actually means contact points between lens and tool. Tool positions are generally defined at the center of a tool, so there is difference between tool path and lens surface. The path was obtained from contact angle and relative position from the contact point. The angle could be calculated after differentiating an aspheric equation and complex algebraic operations. The assumption of the control algorithm was that x moves by constant velocity while z velocity varies. X was normal to the radial direction of lens, but z was tangential. The z velocities and accelerations were determined from current error and next position in each step. In the experiment, accuracy of the control algorithm was checked on a micro-precision machine. The result showed that the control error tended to be diminished when the tool diameter increased, and the error was under sub-micro level.