• Proceedings of the Korean Geotechical Society Conference
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• 2006.03a
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• pp.738-743
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• 2006

Falling rocks are classed by the collapse to wide meaning. it is a kinds of earth disaster that has happen every year. Falling rocks are defined as blocks which had fallen from the cliff. It is caused by the relaxation of discontinuous structures like as a joint, a foliation, a bedding, and so on. Usually, the Relaxation of blocks from the rock face is happened by various kinds factors that are acted as a complex. Sometimes, the tree can be a factor of the weakness or relaxation of rock blocks and a cause of the falling rock.

• Journal of the Korea Society for Simulation
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• v.14 no.4
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• pp.55-68
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• 2005

The advancement in semiconductor technology is leading toward smaller critical dimension designs and larger wafer manufactures. Due to such phenomena, semiconductor industry is in need of an accurate control of the process. Photolithography is one of the key processes where the pattern of each layer is formed. In this process, precise superposition of the current layer to the previous layer is critical. Therefore overlay parameters of the semiconductor photolithography process is targeted for this research. The complex relationship among the input parameters and the output metrologies is difficult to understand and harder yet to model. Because of the superiority in modeling multi-nonlinear relationships, neural networks is used for the simulator modeling. For training the neural networks, conjugate gradient method is employed. An experiment is performed to evaluate the performance among the proposed neural network simulator, stepwise regression model, and the currently practiced prediction model from the test site.

• Journal of the Korean Society for Nondestructive Testing
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• v.28 no.1
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• pp.54-58
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• 2008

Time reversal (TR) of body waves in fluids and isotropic solids has been used in many applications including ultrasonic NDE. However, the study of the TR method for anisotropic materials is not well established. In this paper, the full reconstruction of the input signal is investigated for anisotropic media using an analytical formulation, called a modular Gaussian beam (MGB) model. The time reversal operation of this model in the frequency domain is done by taking the complex conjugate of the Gaussian amplitude and phase received at the TR mirror position. A narrowband reference signal having a particular frequency and number of cycles is then multiplied and the whole signal is inverse Fourier transformed. The original input signal is seen to be fully restored by the TR process of MGB model and this model can be more generalized to simulate the spatial and temporal focusing effects due to TR process in anisotropic materials.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.311-334
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• 2020

The solution of the elliptic partial differential equation has interface singularity at the points which are either the intersections of interfaces or the intersections of interfaces with the boundary of the domain. The singularities that arises in the elliptic interface problems are very complex. In this article we propose an exponentially accurate nonconforming spectral element method for these problems based on [7, 18]. A geometric mesh is used in the neighbourhood of the singularities and the auxiliary map of the form z = ln ξ is introduced to remove the singularities. The method is essentially a least-squares method and the solution can be obtained by solving the normal equations using the preconditioned conjugate gradient method (PCGM) without computing the mass and stiffness matrices. Numerical examples are presented to show the exponential accuracy of the method.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.151-170
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• 2009

Let m be a positive integer. We show that for any given real number ${\alpha}\;{\in}\;[0,\;1]$ and complex number $\mu$ with $|\mu|{\leq}1$ which satisfy $e^{2{\pi}i{\alpha}}{\mu}^m\;{\neq}\;1$, there exists a Blaschke product B of degree 2m + 1 which has a fixed point of multiplier ${\mu}^m$ at the point at infinity such that the restriction of the Blaschke product B on the unit circle is a critical circle map with rotation number $\alpha$. Moreover if the given real number $\alpha$ is irrational of bounded type, then a modified Blaschke product of B is quasiconformally conjugate to some rational function of degree m + 1 which has a fixed point of multiplier ${\mu}^m$ at the point at infinity and a Siegel disk whose boundary is a quasicircle containing its critical point.

• Geophysics and Geophysical Exploration
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• v.1 no.2
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• pp.116-126
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• 1998

I present a datuming scheme for poststack data that uses wavefield depth extrapolation. The method I have developed allows the use of any depth extrapolation technique, such as phase-shift, split-step, and finite-difference extrapolation. I derive the datuming algorithms by transposing and taking the complex conjugate (i.e. taking adjoint) of the corresponding forward modeling operator, which does upward extrapolation from a flat surface to an irregular surface. The exact adjoint relation between the forward modeling operator and the datuming operator is demonstrated algebraically. Testing the poststack datuming algorithms with synthetic data, using several depth extrapolation algorithms, has shown that the method works well.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.405-419
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• 2005

We present some properties characterizing the Mandelbrot set of quadratic rational maps. Any quadratic rational map is conjugate to either $z^2+c$ or ${\lambda}(z+1/z)+b$. For ${\mid}{\lambda}{\mid}=1$, we find the figure of the Mandelbrot set $M_{\lambda}$, the set of parameters b for which the Julia set of ${\lambda}(z+1/z)+b$ is connected. It is seen to be the whole complex plane if ${\lambda}{\neq}1$, but it is intricate fractal if ${\lambda}=1$. This supplements the work already investigated for the case ${\mid}{\lambda}{\mid}>1$.

• Proceedings of the KSME Conference
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• 2008.11b
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• pp.2558-2561
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• 2008

In the present study, a parallel Taylor-Galerkin/level set based two-phase flow code was developed using finite element discretization and domain decomposition method based on MPI (Message Passing Interface). The proposed method can be utilized for the analysis of a large scale free surface problem in a complex geometry due to the feature of FEM and domain decomposition method. Four-step fractional step method was used for the solution of the incompressible Navier-Stokes equations and Taylor-Galerkin method was adopted for the discretization of hyperbolic type redistancing and advection equations. A Parallel ILU(0) type preconditioner was chosen to accelerate the convergence of a conjugate gradient type iterative solvers. From the present parallel numerical experiments, it has been shown that the proposed method is applicable to the simulation of large scale free surface flows.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.2
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• pp.164-173
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• 1994

A numerical model to solve mild slope equation is developed by use of a preconditioned conjugate gradient method (PCGM). In the present paper. accurate boundary conditions and a better preconditioner are employed which are improved from the existing method of Panchang et al. (1991). Computational procedures are focused on weakly nonlinear waves, and emerged problems to make a more accurate model are discussed. The results of model are tested against laboratory results of both circular and elliptic shoals. Model results of wave amplitude show excellent agreement with laboratory data and thes thus model can be used as a powerful tool to calculate wave transformation in shallow waters with complex bathymetry.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.19 no.1
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• pp.71-78
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• 1983

A method is given for obtaining low-order models for a linear time-invariant system of high-order by minimizing a functional of the reduction error between the output response of the original system and the low-order model. The method is based on the Astrom's algorithm for the evaluation of complex integrals and the conjugate gradient method of Fletcher-Reeves. An example illustrating the application of this method is given for approximation of a 4-th order system to be used in the load frequency control of generator systems.