• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 추계학술대회
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• pp.73-78
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• 2004

In this research, the photoelastic experimental hybrid method with Hook-Jeeves numerical method has been developed: This method is more precise and stable than the photoelastic experimental hybrid method with Newton-Rapson numerical method with Gaussian elimination method. Using the photoelastic experimental hybrid method with Hook-Jeeves numerical method, we can separate stress components from isochromatics only and stress intensity factors and stress concentration factors can be determined. The photoelastic experimental hybrid method with Hook-Jeeves had better be used in the full field experiment than the photoelastic experimental hybrid method with Newton-Rapson with Gaussian elimination method.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.1249-1253
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• 2001

Numerical analysis is sometimes used to solve the problems in the engineering and natural science fields. On this reason, the faster, more practical system in computing the numerical solution is required. This paper deals with the numerical evaluation of various numerical integration methods which is frequently used in the engineering fields. This paper choices four integration methods such as Euler method, Heun's method, Runge-Kutta method and Gill's method for evaluating the each integration method. In numerical examples, the free vibration problem on an elastic foundation is chosen. As the numerical results, the natural frequencies and the running time are obtained, and these results are compared to examine the practicality of integration methods.

• 한국전자파학회논문지
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• 제7권4호
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• pp.328-335
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• 1996

The numerical dispersive characteristics and the numerical stability confition of the Multi-Resolution Time-Domain(MRTD) method are calculated. A dispersion analysis of the MRTD schemes including a comparison to Yee's Finite-Difference Time-Domain(FDTD) method is given. The superiority of the MRTD method to the spatial discretization is shown. The required computational memory can be reduced by using the MRTD method. We expect that the MRTD method will be very useful method for numerical modelling of electromagnetics.

• Journal of Mechanical Science and Technology
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• 제20권1호
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• pp.94-109
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• 2006

An improved meshfree method called the Petrov-Galerkin natural element (PG-NE) method is introduced in order to secure the numerical integration accuracy. As in the Bubnov-Galerkin natural element (BG-NE) method, we use Laplace interpolation function for the trial basis function and Delaunay triangles to define a regular integration background mesh. But, unlike the BG-NE method, the test basis function is differently chosen, based on the Petrov-Galerkin concept, such that its support coincides exactly with a regular integration region in background mesh. Illustrative numerical experiments verify that the present method successfully prevents the numerical accuracy deterioration stemming from the numerical integration error.

• 한국해양공학회지
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• 제16권1호
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• pp.22-26
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• 2002

In this paper, a finite element method is applied to the numerical calculation of the harbor calmness. The mild stop equation as the basic equation is used. The key of this model is that the bottom friction and boundary absorption are imposed. A numerical result is presented and compared with the results obtained from the other numerical analysis. These results are in very well agreement. This method calculating the calmness can be broadly utilized making the new design of harbor and fishing port in the future.

• 한국안전학회지
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• 제35권3호
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• pp.49-57
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• 2020

In comparison with the existing static reliability analysis methods, the dynamic reliability analysis(DyRA) method is more suitable for estimating the failure probability of a structure subjected to earthquake excitations because it can take into account the frequency characteristics and damping capacity of the structure. However, the DyRA is known to have an issue of numerical stability due to the uncertainty in random sampling of the earthquake excitations. In order to solve this numerical stability issue in the DyRA approach, this study proposed two earthquake-scale factors. The first factor is defined as the ratio of the first earthquake excitation over the maximum value of the remaining excitations, and the second factor is defined as the condition number of the matrix consisting of the earthquake excitations. Then, we have performed parametric studies of two factors on numerical stability of the DyRA method. In illustrative example, it was clearly confirmed that the two factors can be used to verify the numerical stability of the proposed DyRA method. However, there exists a difference between the two factors. The first factor showed some overlapping region between the stable results and the unstable results so that it requires some additional reliability analysis to guarantee the stability of the DyRA method. On the contrary, the second factor clearly distinguished the stable and unstable results of the DyRA method without any overlapping region. Therefore, the second factor can be said to be better than the first factor as the criterion to determine whether or not the proposed DyRA method guarantees its numerical stability. In addition, the accuracy of the numerical analysis results of the proposed DyRA has been verified in comparison with those of the existing first-order reliability method(FORM), Monte Carlo simulation(MCS) method and subset simulation method(SSM). The comparative results confirmed that the proposed DyRA method can provide accurate and reliable estimation of the structural failure probability while maintaining the superior numerical efficiency over the existing methods.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 추계학술대회
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• pp.492-497
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• 2004

Three methods for design sensitivity such as numerical differentiation, analytical method and semi-analytical method have been developed for the last three decades. Although analytical design sensitivity analysis is exact, it is hard to implement for practical design problems. Therefore, numerical method such as finite difference method is widely used to simply obtain the design sensitivity in most cases. The numerical differentiation is sufficiently accurate and reliable for most linear problems. However, it turns out that the numerical differentiation is inefficient and inaccurate because its computational cost depends on the number of design variables and large numerical errors can be included especially in nonlinear design sensitivity analysis. Thus semi-analytical method is more suitable for complicated design problems. Moreover semi-analytical method is easy to be performed in design procedure, which can be coupled with an analysis solver such as commercial finite element package. In this paper, implementation procedure for the semi-analytical design sensitivity analysis outside of the commercial finite element package is studied and computational technique is proposed, which evaluates the pseudo-load for design sensitivity analysis easily by using the design variation of corresponding internal nodal forces. Errors in semi-analytical design sensitivity analysis are examined and numerical examples are illustrated to confirm the reduction of numerical error considerably.

• 한국해양공학회지
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• 제37권6호
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• pp.256-265
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• 2023

Many numerical methods have been developed since 1961, but unresolved issues remain. This study developed a numerical method to address these issues and determine the coefficients and properties of rotational waves with a shear current in a finite water depth. The number of unknown constants was reduced significantly by introducing a wavelength-independent coordinate system. The reference depth was calculated independently using the shooting method. Therefore, there was no need for partial derivatives with respect to the wavelength and the reference depth, which simplified the numerical formulation. This method had less than half of the unknown constants of the other method because Newton's method only determines the coefficients. The breaking limit was calculated for verification, and the result agreed with the Miche formula. The water particle velocities were calculated, and the results were consistent with the experimental data. Dispersion relations were calculated, and the results are consistent with other numerical findings. The convergence of this method was examined. Although the required series order was reduced significantly, the total error was smaller, with a faster convergence speed.

• Wind and Structures
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• 제18권5호
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• pp.549-566
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• 2014

In spite of progress in the numerical simulation of typhoon wind field in atmospheric boundary layer (ABL), using typhoon wind field model in conjunction with Monte Carlo simulation method can only accurately evaluate typhoon wind field over a general terrain. This method is not enough for a reliable evaluation of typhoon wind field over the actual complex terrain with surface roughness and topography variations. To predict typhoon wind field over the actual complex terrain in ABL, a hybrid numerical simulation method combined typhoon simulation used the typhoon wind field model proposed by Meng et al. (1995) and CFD simulation in which the Reynolds averaged Navier-Stokes (RANS) equations and k-${\varepsilon}$ turbulence model are used. Typhoon wind filed during typhoon Dujuan and Imbudo are simulated using the hybrid numerical simulation method, and compared with the results predicted by the typhoon wind field model and the wind field measurement data collected by Fugro Geotechnical Services (FGS) in Hong Kong at the bridge site from the field monitoring system of wind turbulence parameters (FMS-WTP) to validate the feasibility and accuracy of the hybrid numerical simulation method. The comparison demonstrates that the hybrid numerical simulation method gives more accurate prediction to typhoon wind speed and direction, because the effect of topography is taken into account in the hybrid numerical simulation method.

• Kyungpook Mathematical Journal
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• 제62권4호
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• pp.699-713
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• 2022

This paper proposes a hybrid successive over-relaxation iterative method for the numerical solution of a nonlinear diffusion in a one-dimensional porous medium. The considered mathematical model is discretized using a computational complexity reduction scheme called half-sweep finite differences. The local truncation error and the analysis of the stability of the scheme are discussed. The proposed iterative method, which uses explicit group technique and modified successive over-relaxation, is formulated systematically. This method improves the efficiency of obtaining the solution in terms of total iterations and program elapsed time. The accuracy of the proposed method, which is measured using the magnitude of absolute errors, is promising. Numerical convergence tests of the proposed method are also provided. Some numerical experiments are delivered using initial-boundary value problems to show the superiority of the proposed method against some existing numerical methods.