• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.2
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• pp.197-215
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• 2015

Modeling water flow in variably saturated, porous media is important in many branches of science and engineering. Highly nonlinear relationships between water content and hydraulic conductivity and soil-water pressure result in very steep wetting fronts causing numerical problems. These include poor efficiency when modeling water infiltration into very dry porous media, and numerical oscillation near a steep wetting front. A one-dimensional finite element formulation is developed for the numerical simulation of variably saturated flow systems. First order backward Euler implicit and second order Crank-Nicolson time discretization schemes are adopted as a solution strategy in this formulation based on Picard and Newton iterative techniques. Five examples are used to investigate the numerical performance of two approaches and the different factors are highlighted that can affect their convergence and efficiency. The first test case deals with sharp moisture front that infiltrates into the soil column. It shows the capability of providing a mass-conservative behavior. Saturated conditions are not developed in the second test case. Involving of dry initial condition and steep wetting front are the main numerical complexity of the third test example. Fourth test case is a rapid infiltration of water from the surface, followed by a period of redistribution of the water due to the dynamic boundary condition. The last one-dimensional test case involves flow into a layered soil with variable initial conditions. The numerical results indicate that the Crank-Nicolson scheme is inefficient compared to fully implicit backward Euler scheme for the layered soil problem but offers same accuracy for the other homogeneous soil cases.

• Geomechanics and Engineering
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• v.7 no.4
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• pp.375-401
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• 2014

It is generally accepted that material heterogeneity has a great influence on the deformation, strength, damage and failure modes of rock. This paper presents numerical simulation on rock failure process based on the characterization of rock heterogeneity by using a digital image processing (DIP) technique. The actual heterogeneity of rock at mesoscopic scale (characterized as minerals) is retrieved by using a vectorization transformation method based on the digital image of rock surface, and it is imported into a well-established numerical code Rock Failure Process Analysis (RFPA), in order to examine the effect of rock heterogeneity on the rock failure process. In this regard, the numerical model of rock could be built based on the actual characterization of the heterogeneity of rock at the meso-scale. Then, the images of granite are taken as an example to illustrate the implementation of DIP technique in simulating the rock failure process. Three numerical examples are presented to demonstrate the impact of actual rock heterogeneity due to spatial distribution of constituent mineral grains (e.g., feldspar, quartz and mica) on the macro-scale mechanical response, and the associated rock failure mechanism at the meso-scale level is clarified. The numerical results indicate that the shape and distribution of constituent mineral grains have a pronounced impact on stress distribution and concentration, which may further control the failure process of granite. The proposed method provides an efficient tool for studying the mechanical behaviors of heterogeneous rock and rock-like materials whose failure processes are strongly influenced by material heterogeneity.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.505-511
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• 2007

Recently, the equivalent relations between a symmetric dual problem and a matrix game B(x, y) were given in [6: D.S. Kim and K. Noh, J. Math. Anal. Appl. 298(2004), 1-13]. Using more simpler form of B(x, y) than one in [6], we establish the equivalence relations between a symmetric dual problem and a matrix game, and then give a numerical example illustrating our equivalence results.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.379-389
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• 2000

FORD and FULKERSON have shown that a stationary maximal dynamic flow can be obtained by solving a transhipment problem associated with the static network and thereby finding the maximal temporally repeated dynamic flow. This flow is known to be an optimal dynamic flow. this paper presents the remark that temporally repeated flows may be not optimal for a minimal dynamic flow and an algorithm for such a flow. a numerical example is presented.

• International Journal of Control, Automation, and Systems
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• v.5 no.4
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• pp.372-378
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• 2007

This paper discusses Robust $H{\infty}$ control problems for networked control systems (NCSs) with time delays and subject to norm-bounded parameter uncertainties. Based on a new discrete-time model, two approaches of robust controller design are proposed. A numerical example and experimental verification with an NCS test bed are given to illustrate the feasibility and effectiveness of proposed design methodologies.

• Journal of the military operations research society of Korea
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• v.11 no.2
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• pp.53-63
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• 1985

This paper presents a multi-costraint optimization model for redundant system reliability. The optimization model is usually formulated as a nonlinear integer programming (NIP) problem. This paper reformulates the NIP problem into a linear integer programming (LIP) problem. Then an efficient 'Branch and Straddle' algorithm is proposed to solve the LIP problem. The efficiency of this algorithm stems from the simultaneous handling of multiple variables, unlike in ordinary branch and bound algorithms. A numerical example is given to illustrate this algorithm.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.35-45
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• 2008

In cases sufficient conditions for the semilocal convergence of Newtonlike methods are violated, we start with a modified Newton-like method (whose weaker convergence conditions hold) until we stop at a certain finite step. Then using as a starting guess the point found above we show convergence of the Newtonlike method to a locally unique solution of a nonlinear operator equation in a Banach space setting. A numerical example is also provided.

• Management Science and Financial Engineering
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• v.14 no.2
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• pp.25-44
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• 2008

This paper concentrates on reduction of a Quadratic Fractional Integer Programming Problem (QFIP) to a 0-1 Mixed Linear Programming Problem (0-1 MLP). The solution technique is based on converting the integer variables to binary variables and then the resulting Quadratic Fractional 0-1 Programming Problem is linearized to a 0-1 Mixed Linear Programming problem. It is illustrated with the help of a numerical example and is solved using the LINDO software.

• Proceedings of the KIEE Conference
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• 2008.04a
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• pp.207-208
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• 2008

This paper presents a robust state observer design for a class of Lipschitz nonlinear systems with time delay and external disturbance. A sufficient conditions on the existence of the proposed observer are characterized by linear matrix inequalities. It is also shown that the proposed observer design can reduce the effect on the estimation error of external disturbance up to the prescribed level in spite of the existence of time delay. Finally, a numerical example is provided to verify the proposed design method.

• Structural Engineering and Mechanics
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• v.20 no.2
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• pp.209-223
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• 2005

A new method for deriving analytical solution of the annular elastic plate on elastic foundation under axisymmetric loading is presented. The formulation is based on application of Hankel integral transforms and Bessel functions' properties in the corresponding boundary-value problem. A representative example is studied and the obtained solution is compared with published numerical results indicating excellent agreement.