• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.567-584
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• 2014

In this paper, we consider approximation of eigenelements of a two dimensional compact integral operator with a smooth kernel by discrete collocation and iterated discrete collocation methods. By choosing numerical quadrature appropriately, we obtain convergence rates for gap between the spectral subspaces, and also we obtain superconvergence rates for eigenvalues and iterated eigenvectors. We then apply Richardson extrapolation to obtain further improved error bounds for the eigenvalues. Numerical examples are presented to illustrate theoretical estimates.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.133-142
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• 2000

We consider some numerical solution methods for equilibrium equations Af + E$^{T}$ λ = r, Ef = s. Algebraic problems of this form evolve from many applications such as structural optimization, fluid flow, and circuits. An important approach, called the force method, to the solution to such problems involves dimension reduction nullspace computation for E. The purpose of this paper is to investigate the substructuring method for the solution step of the force method in the context of the incompressible fluid flow. We also suggests some iterative methods based upon substructuring scheme..

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.449-465
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• 1994

The two common numerical methods to approximate the solution of partial differential equations are the finite element method and the finite difference method. They both lead to solving large sparse linear systems. For many applications, it is not unusal that the order of matrix is greater than 10, 000. For this kind of problem, a direct method such as Gaussian elimination can not be used because of the prohibitive cost. To this end, many iterative methods with modest cost have been studied and proposed by numerical analysts.(omitted)

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1998.10a
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• pp.36-43
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• 1998

The purpose of study is to propose numerical assessment methods of lateral deformation shape under lateral loads for regular high-rise buildings. The normalized 1st mode shape is used to assess lateral deformation shape. The assessment method are mass participation factor, representative value by RMS, the mean value, median of the nomalized 1st mode shape. These methods are able to know a fundamental lateral deformation shape of the building and effects of interactive systems numerically. Generally the characteristics of normalized 1st mode shape for various models coincide with numerical assessment results.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.157-172
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• 1998

A numerical method is proposed for dynamical systems. We utilize the fact that special matrix exponentials can be exactly evaluated by the intrinsic library functions. Numerical examples are given, which show that the relative error s of the proposed method converge to a small constant and that the method faithfully approximates the dynamics of the nonlinear differential equations.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.177-183
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• 1988

In this work, two numerical schemes arc proposed for solving a general form of Cauchy problem. Here, the problem, to be defined, consists of a system of Volterra integro-differential equations. Picard's and Seiddl'a methods of successive approximations are ued to obtain the approximate solution. The convergence of these approximations is established and the rate of convergence is estimated in every case.

• Geomechanics and Engineering
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• v.12 no.6
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• pp.1003-1020
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• 2017

Estimation of groundwater inflow into underground opening is of critical importance for the design and construction of underground structures. Groundwater inflow into a pilot underground storage facility in China was estimated using analytical equations, numerical modeling and field measurement. The applicability of analytical and numerical methods was examined by comparing the estimated and measured results. Field geological investigation indicated that in local scale the high groundwater inflows are associated with the appearance of open joints, fractured zone or dykes induced by shear and/or tensile tectonic stresses. It was found that 8 groundwater inflow spots with high inflow rates account for about 82% of the total rate for the 9 caverns. On the prediction of the magnitude of groundwater inflow rate, it was found that could both (Finite Element Method) FEM and (Discrete Element Method) DEM perform better than analytical equations, due to the fact that in analytical equations simplified assumptions were adopted. However, on the prediction of the spatial distribution estimation of groundwater inflow, both analytical and numerical methods failed to predict at the present state. Nevertheless, numerical simulations would prevail over analytical methods to predict the distribution if more details in the simulations were taken into consideration.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2006.10a
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• pp.157-165
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• 2006

In February,2004, at International Maritime Organization (IMO), LONDON, a new international convention 'International Convention fur the Control and Management of Ship's Ballast Water and Sediment 2004' was adopted. It is called 'Ballast Water Management Convention (BWM)'. Ballast water means charged seawater or fresh water in ship's special tanks (ballast tank) to keep safety navigation and ship's maneuverability. However, from 1980, it was point out the serious problem for marine ecosystem and human life that ballast water includes harmful marine species (and small organisms) and these species are also discharged along with ballast water. These species were released with discharged ballast water in water areas, where species are different from discharged ballast water. The problem is that released species increase when released species are more powerful than native species and consequently, marine ecological system is destroyed in released water area. Authors have inspected the validity of the ballast water exchange using pumping-through method that is one of the methods of ballast water management. In this paper, the numerical simulation of the motion and density of the fluid at the time of exchange of the fluid in a 2-dimensional tank using the pumping-through method was carried out by using two different type numerical methods. One method is MPS method that is one of the particle methods. Other one is Finite Different Method (FDM). Authors were compared with result of two numerical method calculations and experiment result and reported some knowledge from these results.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2929-2934
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• 2007

Prediction methods for cavitation noise are presented. At first, direct numerical simulation of cavitating flow noise has been performed, and acoustic analogy equation based on the cavitation noise modeling is derived. For the direct numerical simulation, a density based homogenous equilibrium model is employed to simulate cavitating two-phase flow and the governing equations are solved with high-order numerical schemes to resolve cavitation noise. The compressible Navier-Stokes equations for mixture fluids are discretized with a sixth-order central compact scheme, and the steep gradient of flow variables and supersonic regions are treated with the selective spatial filtering technique. The direct simulation of cavitating flow noise is performed for a 2D circular cylinder at cavitation number 0.7 and 1. The far-field noise is also predicted with the derived analogy equation. Noise spectrum predicted with the equation is well compared with the result of direct numerical simulation and also agree well with the theory.

• Tunnel and Underground Space
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• v.2 no.1
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• pp.152-163
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• 1992

The study of rock mass behaviour through a numerical analysis is important for the design, construction and maintenance of large rock caverns. The objectives of the numerical analysis are to design reasonably and construct safely the underground structures, to maintain them soundly after construction and to extend them securely for a desired period of time. Methods of numerical analyses included in this case study are the finite element method, the boundary element method, and the distinct element method. The numerical models are purely elastic, elastoplastic, visco-elastic, visco-plastic, easto-visco-plastic and jointed-discontinuous materials. The results of this case study indicate that the rock mass behaviour could be predicted exactly through continuous comparisons of the numerical results with the in-situ measurements.