• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.2
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• pp.69-79
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• 2008

Multigrid methods finite element/finite volume methods and their convergence properties are reviewed in a general setting. Some early theoretical results in simple finite element methods in variational setting method are given and extension to nonnested-noninherited forms are presented. Finally, the parallel theory for nonconforming element[13] and for cell centered finite difference methods [15, 23] are discussed.

• Proceedings of the Korean Geotechical Society Conference
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• 2000.11a
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• pp.665-672
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• 2000

The problems of discontinuous layer interface are very important in the algorithm and programming for the analysis of multi-layered consolidation using a numerical analysis, finite difference method(F.D,M.). Better results can be obtained by the process for discontinuous layer interface, since it can help consolidation analysis to model the actual ground Explicit method is simple for analysis algorithm and convenient for use except for applying the operator Crank-Nicolson method represents implicit method, which have different analysis method according to weighting factor. This method uses different algorithm according to dimension. And, this paper uses alternative direction implicit method. The purpose of this paper provides an efficient computer algorithm based on numerical analysis using finite difference method which account for multi-layered soils with confined aquifer to determine the degree of consolidation and excess pore pressures relative to time and positions more realistically.

• Journal of Ocean Engineering and Technology
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• v.16 no.5
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• pp.15-20
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• 2002

In this research, the finite difference lattice Boltzmann method(FDLBM) is used to analyze gravity currents in the lock exchange configuration that occur in many natural and man-made situations. At a lock those are seen when a gate is suddenly opened, and, in the atmosphere, when the thunderstorm outflows make a cold front. At estuaries in the ocean, the phenomenon is found between fresh water from a river and salt water in the sea. Since such interesting phenomena were recognized, pioneers have challenged to make them clear by conducing both experiments and analysis. Most of them were about the currents of liquid or Boussinesq fluids, which are assumed as incompressible. Otherwise, the difference in density of two fluids is small. The finite difference lattice Boltzmann method has been a powerful tool to simulate the flow of compressible fluids. Also, numerical predictions using FDLBM to clarify the gravity currents of compressible fluids exhibit all features, but typically observed in experimental flows near the gravity current head, including the lobe-and-cleft structure at the leading edge.

• Geophysics and Geophysical Exploration
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• v.6 no.2
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• pp.77-86
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• 2003

We designed a new time-domain, finite-difference, elastic wave modeling technique, based on a displacement formulation. which yields nearly correct solutions to Lamb's problem. Unlike the conventional, displacement-based, finite-difference method using a node-based grid set (where both displacements and material properties such as density and Lame constants are assigned to nodal points), in our new finite-difference method, we use a cell-based grid set (where displacements are still defined at nodal points but material properties within cells). In the case of using the cell-based grid set, stress-free conditions at the free surface are naturally described by the changes in the material properties without any additional free-surface boundary condition. Through numerical tests, we confirmed that the new second-order finite differences formulated in the cell-based grid let generate numerical solutions compatible with analytic solutions unlike the old second-order finite-differences formulated in the node-based grid set.

• Journal of Mechanical Science and Technology
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• v.16 no.10
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• pp.1327-1335
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• 2002

The shock wave process represents an abrupt change in fluid properties, in which finite variations in pressure, temperature, and density occur over the shock thickness which is comparable to the mean free path of the gas molecules involved. This shock wave fluid phenomenon is simulated by using the finite difference lattice Boltzmann method (FDLBM). In this paper, a new model is proposed using the lattice BGK compressible fluid model in FDLBM for the purpose of speeding up the calculation as well as stabilizing the numerical scheme. The numerical results of the proposed model show good agreement with the theoretical predictions.

• Proceedings of the KSME Conference
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• 2001.11b
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• pp.468-474
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• 2001

The shock process represents an abrupt change in fluid properties, in which finite variations in pressure, temperature, and density occur over a shock thickness which is comparable to the mean tree path of the gas molecules involved. The fluid phenomenon is simulated by using finite difference lattice Boltzmann method (FDLBM). In this research, the new model is proposed using the lattice BGK compressible fluid model in FDLBM for the purpose of shortening in calculation time and stabilizing in simulation operation. The numerical results agree also with the theoretical predictions.

• International Journal of Safety
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• v.1 no.1
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• pp.13-17
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• 2002

A new system of equations governing the nonlinear thin laminated plates with large deflections using von Karman equations is derived. The effects of transverse shear in the thin interlayer are included as part of the analysis. The finite difference method is used to perform the geometrically nonlinear behavior of the plate. The resultant equations permit the analysis of the effect of transverse shear stress deformation on the overall behavior of the interlayer using the load incremental method. For the purpose of feasibility and validity of this present method, the numerical results are compared with other available solutions for accuracy as well as efficiency. The solution techniques have been implemented and the numerical results of example problem are discussed and evaluated.

• 한국전산유체공학회:학술대회논문집
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• 2006.10a
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• pp.22-25
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• 2006

Direct simulations of aerodynamic sound, especially sound emitted by rapidly rotating elliptic cylinder by the finite difference lattice Boltzmann method (FDLBM). Effect of pile-fabrics for noise reduction is also studied by the finite volume LBM (FVLBM) using an unstructured grid. Second order time integration and third order upwind scheme are shown to be enough for these simulations. Sound sources are detected to be doublets for both cases. For the elliptic cylinder, the doublet is generated in the interaction between the vortex and the edge. For the circular cylinders, they are generated synchronizing with the Karman vortex street, and it is also shown that the pile-fabrics covering the surface of the cylinder reduces the strength of the source.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.8 s.239
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• pp.903-910
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• 2005

Inverse radiation problems are solved for estimating the boundary conditions such as temperature distribution and wall emissivity in axisymmetric absorbing, emitting and scattering medium, given the measured incident radiative heat fluxes. Various regularization methods, such as hybrid genetic algorithm, conjugate-gradient method and finite-difference Newton method, were adopted to solve the inverse problem, while discussing their features in terms of estimation accuracy and computational efficiency. Additionally, we propose a new combined approach that adopts the hybrid genetic algorithm as an initial value selector and uses the finite-difference Newton method as an optimization procedure.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.329-341
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• 2021

In this study, we consider an efficient and accurate finite difference method for the four underlying asset equity-linked securities (ELS). The numerical method is based on the operator splitting method with non-uniform grids for the underlying assets. Even though the numerical scheme is implicit, we solve the system of discrete equations in explicit manner using the Thomas algorithm for the tri-diagonal matrix resulting from the system of discrete equations. Therefore, we can use a relatively large time step and the computation of the ELS option pricing is fast. We perform characteristic computational test. The numerical test confirm the usefulness of the proposed method for pricing the four underlying asset equity-linked securities.