• 한국전산유체공학회:학술대회논문집
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• 2007.04a
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• pp.30-40
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• 2007

The implicit discontinuous Galerkin method for the two-dimensional Euler equations was developed on unstructured triangular meshes, which can achieve higher-order accuracy by wing hierachical basis functions based on Legendre polynomials. Numerical tests were conducted to estimate the convergence order of numerical solutions to the Ringleb flow and the supersonic vortex flow for which analytic solutions are available. And, the flows around a circle and a NACA0012 airfoil was also numerically simulated. Numerical results show that the implicit discontinuous Galerkin methods with higher-order representation of curved solid boundaries can be an efficient higher-order method to obtain very accurate numerical solutions on unstructured meshes.

• Communications for Statistical Applications and Methods
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• v.19 no.2
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• pp.267-276
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• 2012

Bagai et al. (1989) proposed a distribution-free test for stochastic ordering in the competing risk model, and recently Murakami (2009) utilized a standard saddlepoint approximation to provide tail probabilities for the Bagai statistic under finite sample sizes. In the present paper, we consider the Gaussian-polynomial approximation proposed in Ha and Provost (2007) and compare it to the saddlepoint approximation in terms of approximating the percentiles of the Bagai statistic. We make numerical comparisons of these approximations for moderate sample sizes as was done in Murakami (2009). From the numerical results, it was observed that the Gaussianpolynomial approximation provides comparable or greater accuracy in the tail probabilities than the saddlepoint approximation. Unlike saddlepoint approximation, the Gaussian-polynomial approximation provides a simple explicit representation of the approximated density function. We also discuss the details of computations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.27-39
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• 1998

We describe a fast numerical method for non-separable elliptic equations in self-adjoin form on irregular adaptive domains. One of the most successful results in numerical PDE is developing rapid elliptic solvers for separable EPDEs, for example, Fourier transformation methods for Poisson problem on a square, however, it is known that there is no rapid elliptic solvers capable of solving a general nonseparable problems. It is the purpose of this paper to present an iterative solver for linear EPDEs in self-adjoint form. The scheme discussed in this paper solves a given non-separable equation using a sequence of solutions of Poisson equations, therefore, the most important key for such a method is having a good Poison solver. High performance is achieved by using a fast high-order adaptive Poisson solver which requires only about 500 floating point operations per gridpoint in order to obtain machine precision for both the computed solution and its partial derivatives. A few numerical examples have been presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.1
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• pp.41-53
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• 2008

Polynomials are one of most important and widely used numerical tools in dealing with a smooth function on a bounded domain and trigonometric functions work for smooth periodic functions. However, they are not the best choice if a function has a bounded support in space and in frequency domain. The Prolate Spheroidal wave function (PSWF) of order zero has been known as a best candidate as a basis for band-limited functions. In this paper, we review some basic properties of PSWFs defined as eigenfunctions of bounded Fourier transformation. We also propose numerical inversion schemes based on PSWF and present some numerical examples to show their feasibilities as signal processing tools.

• Structural Engineering and Mechanics
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• v.9 no.6
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• pp.557-568
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• 2000

As time-variant reliability approaches become increasingly used for service life prediction of the aging infrastructure, the demand for computer solution methods continues to increase. Effcient computer techniques have become well established for the reliability analysis of structural systems. Thus far, however, this is largely limited to time-invariant reliability problems. Therefore, the requirements for time-variant reliability prediction of deteriorating structural systems under time-variant loads have remained incomplete. This study presents a computer program for $\underline{REL}$iability of $\underline{T}$ime-Variant $\underline{SYS}$tems, RELTSYS. This program uses a combined technique of adaptive importance sampling, numerical integration, and fault tree analysis to compute time-variant reliabilities of individual components and systems. Time-invariant quantities are generated using Monte Carlo simulation, whereas time-variant quantities are evaluated using numerical integration. Load distribution and post-failure redistribution are considered using fault tree analysis. The strengths and limitations of RELTSYS are presented via a numerical example.

• Proceedings of the KIEE Conference
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• 2000.07b
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• pp.831-833
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• 2000

In this paper, a numerical analysis algorithm of eddy current testing(ECT) for heat exchanger tube with axi-symmetric defects using finite element method(FEM) is presented. In the ECT FEM analysis, we used trianglular and rectangular elements for exact signal of ECT for variable shape of defects. This paper presents a systematic and efficient numerical analysis algorithm for ECT. We employ the LU decomposition and Cholesky method for solving the system matrix. This numerical analysis algorithm is effectively applied to heat exchanger tube with defects.

• 한국전산유체공학회:학술대회논문집
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• 2002.05a
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• pp.17-22
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• 2002

This paper describes numerical research on transverse jet behind rearward-facing step in turbulent supersonic flowfields without chemical reaction. The purpose of transverse jet behind rearward-facing step is to improve mixing of the fuel in the combustor. Two-dimensional unsteady flowfields generated by slot injection into supersonic flow are numerically simulated by integration of Navier-Stokes equation. Final-scale turbulence effects are modeled with two-equation $\kappa-\epsilon$ model. Numerical methods are modeled high-order upwind TVDschemes. A total of 4 cases are computed, comprising slot momentum flux ratios at four step heights downstream of the step. These numerical results are represented periodic phenomenon in unsteady flowfields.

• Structural Engineering and Mechanics
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• v.54 no.3
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• pp.475-489
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• 2015

This study presents the validation of a numerical model developed for dynamic analysis of buildings with roller seismic isolation bearings. Experimental methods allowed validation of the motion equations of a physical model of a building with and without roller bearings under base excitation. The results are presented in terms of modal parameters, frequency response functions (FRFs) and acceleration response. The agreement between numerical and experimental results proves the accuracy of the developed numerical model. Finally, the performance of the constructed seismic protection system is assessed through a parametric study.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.04a
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• pp.3-10
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• 1997

Meshless particle method is a numerical technique which does not use the concept of element. This method can easily handle special engineering problems which cause difficulty in the use of finite element method, however it has a drawback that essential boundary condition is not satisfied. In this paper, several studies for satisfying essential boundary conditions and enhancing the accuracy of solutions are discussed. Particular emphasis is placed on a new numerical technique in which finite elements are used on the boundaries to satisfy the essential boundary conditions and meshless particle method is used in the interior domain. For coupling of the two methods interface elements are introduced into the zone between the subdomains using meshless particle method and finite element method. The shape functions and the approximated displacement functions of the interface element are derived with the ramp function based on the shape function of finite elements. The whole numerical procedures are formulated by Galerkin method. Several numerical examples for enhancing the accuracy of solution in the meshless particle method and a new coupling method are presented.

• International Journal of Naval Architecture and Ocean Engineering
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• v.9 no.2
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• pp.209-218
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• 2017

Sea ice is the main factor affecting the safety of the Arctic engineering. However, traditional numerical methods derived from classical continuum mechanics have difficulties in resolving discontinuous problems like ice damage. In this paper, a non-local, meshfree numerical method called "peridynamics", which is based on integral form, was applied to simulate the interaction between level ice and a cylindrical, vertical, rigid structure at different velocities. Ice in the simulation was freshwater ice and simplified as elastic-brittle material with a linear elastic constitutive model and critical equivalent strain criterion for material failure in state-based peridynamics. The ice forces obtained from peridynamic simulation are in the same order as experimental data. Numerical visualization shows advantages of applying peridynamics on ice damage. To study the repetitive nature of ice force, damage zone lengths of crushing failure were computed and conclude that damage zone lengths are 0.15-0.2 times as ice thickness.