• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.507-528
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• 2022

We propose a path integral method to construct a time stepwise local volatility for the stock index market under Dupire's model. Our method is focused on the pricing with the Monte Carlo Method (MCM). We solve the problem of randomness of MCM by applying numerical integration. We reconstruct this task as a matrix equation. Our method provides the analytic Jacobian and Hessian required by the nonlinear optimization solver, resulting in stable and fast calculations.

• Journal of Advanced Marine Engineering and Technology
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• v.34 no.7
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• pp.943-950
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• 2010

An efficient meshfree method based on a stabilized conforming nodal integration method is developed for elastoplastic contact analysis of metal forming processes. In this approach, strain smoothing stabilization is introduced to eliminate spatial instability in Galerkin meshfree methods when the weak form is integrated by a nodal integration. The gradient matrix associated with strain smoothing satisfies the integration constraint for linear exactness in the Galerkin approximation. Strain smoothing formulation and numerical procedures for path-dependent problems are introduced. Applications of metal forming analysis are presented, from which the computational efficiency has been improved significantly without loss of accuracy.

• Journal of the Korean Society of Safety
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• v.11 no.2
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• pp.16-24
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• 1996

In this study we simulate the fatigue test of a compact tension specimen and obtain the displacements, stresses and strains by using the finite element method. And we examine the path independency of $\Delta$J integral values and compare it with $\Delta$J integral values calculated from load-load line displacement curve. From the results of this study, we can find that $\Delta$J integral show the path Independency for saturated materials. We can also find that the path independency of $\Delta$J Is not satisfied when different material Is assumed near the crack tip, but the difference in $\Delta$J is small. And $\Delta$J integral values calculated from load-load line displacement is very analogous with those from integration path but always have lower values than those from integration paths. In the case of crack closing, we found that $\Delta$J integral values from load-load line displacement should be calculated with the load Increment values based on the crack opening point. The unsaturated material is also simulated and its $\Delta$J shows different values according to the path, but the difference is small.

• Proceedings of the Korea Electromagnetic Engineering Society Conference
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• 2003.11a
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• pp.64-68
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• 2003

For the purpose of the efficient derivation of the closed-form Green's functions by which MoM matrix elements can be analytically evaluated, the optimum approximation path which is deformed from the Sommerfeld integration path on the complex $k_{\rho}$-plane is proposed based upon the steepest descent method and three level approximation procedure.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.04a
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• pp.573-577
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• 1995

An integration method for the hypersingular kernels, in the boundary integralequations used for the solution of crack-like problems in elasticity, has been developed. To isolate the stronger singularities, the actual boundaries are replaced by the smoothly curved auxiliary boundaries which provide the detoured, non-singular integration paths. The auxiliary boundary can be interpreted as a contracted form of the actual boundaries except for the singular element where the collocating point is located. For an optimal integration path for every singular collocation point, the auxiliary boundary may have different shape depending on the position of the collocation point on the singular element.

• Geotechnical Engineering
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• v.14 no.4
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• pp.129-140
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• 1998

Elasto-plastic finite element analysis of geotechnical boundary value problems necessitate the stress integration for the known strain increments. For the elasto-plastic constitutive model, the stress integration is generally achieved by numerical schemes, because analytical integration is impossible for general strain path. In this case, the accuracy of numerical stress integration has an important role on the overall accuracy of nonlinear finite element solution. In this study, the Sloan's substepping method which is one of explicit integration methods has been adopted and iris applicability has been checked. The unstability and inaccuracy of ifs results initiated from initial stress level were revealed. So. a new modified numerical integration method which employs the basic concept of modified Euler scheme for error control is proposed and accuracy and stability of the solutions are confirmed by triaxial test simulation.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.16 no.4 s.95
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• pp.418-426
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• 2005

Based upon three level approximation and the steepest descent path(SDP) method, we consider an optimum choice of approximation path for derivation of new class of closed-flrm Green's functions which can lead to the analytic evaluation of MoM(Method of Moment) matrix elements. It is observed that the present method can give more accurate evaluation of the spatial Green's functions than the previous method, even without the advance investigation of the spectral functions, over a wide frequency range. In order to check the validity of the present method, some numerical results are presented.

• Proceedings of the Korean Information Science Society Conference
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• 2004.10c
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• pp.577-579
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• 2004

Because the Resource reservation Protocol (RSVP) was originally designed fur stationary networks, it is insufficient to accommodate Mobile Nodes (MNs) which frequently change their points of attachment.7his paper deals with how to integrate the RSVP and Hierarchical MHv6 (HMIPv6), in order to quickly establish the QoS guaranteed path and minimize the service disruption when the MN moves around. That can be achieved with the utilization of the common path between the new and old path. Therefore a new method is proposed in detail to find out an anchor node and re-establish a new reservation path.

• Journal of the Korean Society of Visualization
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• v.21 no.2
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• pp.14-23
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• 2023

The pressure difference across stenotic blood vessels is a commonly used clinical metric for diagnosing many cardiovascular diseases. At present, most clinical pressure measurements rely solely on invasive catheterization. In this study, we propose a novel method for non-invasive pressure estimation using the incompressible Navier-Stokes equations and a 3D multi-path integration approach. We verify spatio-temporal convergence on an in-silico dataset of a cylindrical straight pipe phantom with steady and pulsatile flow fields. We then evaluate the proposed method on an in vitro dataset of reconstructed control, pre-operative, and post-operative carotid artery cases acquired from 4D flow MRI. The performance of our method is compared to existing approaches based on the pressure Poisson equation and work-energy relative pressure. The results demonstrate the proposed method's high accuracy, robustness to spatio-temporal subsampling, and reduced sensitivity to noise, highlighting its great potential for non-invasive pressure estimation.

• Journal of Electrical Engineering and Technology
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• v.5 no.4
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• pp.511-521
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• 2010

This paper presents a new algorithm to determine accurate bus-wise transmission loss allocation utilizing path-integrals dictated by the transaction strategy. For any transaction strategy, the total sum of the allocated transmission losses of all buses is equal to the actual loss given by the AC power-flow calculation considering the distributed slack. In this paper, the bus-wise allocation of the transmission loss is calculated by integrating the differential loss along a path determined by the transaction strategy. The proposed algorithm is also compared with Galiana's method, which is the well-known transmission loss allocation algorithm based on integration. The performance of the proposed algorithm is evaluated by case studies carried out on the WSCC 9-bus, IEEE 14-bus, New England 39-bus, and IEEE 118-bus systems. The simulation results show that the proposed algorithm is fast and accurate with a large step size.