• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.755-770
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• 2013

One of the interesting nonlinear matrix equations is the quadratic matrix equation defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix, and A, B and C are $n{\times}n$ given matrices with real elements. Another one is the matrix polynomial $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m=0,\;X,\;A_i{\in}\mathbb{R}^{n{\times}n}$$. Newton's method is used to find the symmetric and bisymmetric solvents of the nonlinear matrix equations Q(X) and P(X). The method does not depend on the singularity of the Fr$\acute{e}$chet derivative. Finally, we give some numerical examples.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.156-161
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• 1998

This describes a numerical method for predicting the incompressible unsteady laminar three-dimensional flows of fluid behaviour with free-surface. The elliptic differential equations governing the flows have been linearized by means of finite-difference approximations, and the resulting equations have been solved via a fully-implicit iterative method. The free-surface is defined by the motion of a set of marker particles and interface behaviour was investigated by way of a 'Lagrangian' technique. Using the GALA concept of Spalding, the conventional mass continuity equation is modified to form a volumetric or bulk-continuity equation. The use of this bulk-continuity relation allows the hydrodynamic variables to be computed over the entire flow domain including both liquid and gas regions. Thus, the free-surface boundary conditions are imposed implicitly and the problem formulation is greatly simplified. The numerical procedure is validated by comparing the predicted results of a periodic standing waves problems with analytic solutions or experimental results from the literature. The results show that this numerical method produces accurate and physically realistic predictions of three-dimensional free-surface flows.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1625-1630
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• 2003

An iterative modal analysis approach is developed to determine the effect of the transverse open cracks and the moving mass on the dynamic behavior of simply supported pipe conveying fluid. The equation of motion is derived by using Lagrange's equation. The influences of the velocity of moving mass, the velocity of fluid flow and a crack have been studied on the dynamic behavior of a simply supported pipe system by numerical method. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. that is, the crack is modelled as a rotational spring. Totally, as the velocity of fluid flow is increased, the mid-span deflection of simply supported pipe conveying fluid is increased. The position of the crack is middle point of the pipe, the mid-span deflection of simply supported pipe presents maximum deflection.

• Computers and Concrete
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• v.1 no.2
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• pp.131-150
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• 2004

We present in this work a coupled phenomenological chemo-mechanical model that represents the degradation of concrete-like materials. The chemical behaviour is described by the nowadays well known simplified calcium leaching approach. And the mechanical damage behaviour is described by a continuum damage model which involves the gradient of the damage quantity. The coupled nonlinear problem at hand is addressed within the context of the finite element method. For the equation governing the calcium dissolution-diffusion part of the problem, special care is taken to treat the highly nonlinear calcium conductivity and solid calcium functions. The algorithmic design is based on a Newton-type iterative scheme where use is made of a recently proposed relaxed linearization procedure. And for the equation governing the damage part of the problem, an augmented Lagrangian formulation is used to take into account the damage irreversibility constraint. Finally, numerical simulations are compared with experimental results on cement paste.

• Journal of the Korean institute of surface engineering
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• v.24 no.3
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• pp.125-136
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• 1991

a mathematical model is presented to describe the current distribution on a rotaing disk electrode under the galvanostatic pulse conlitions. A numerical technique by finite difference method to the transient convective diffusion equation, coordinate transformation and separation of variables to Laplace equation, and an iterative algorithm to solve the above equations simtltaneously with approximate boundary conditions were developed. An experimental investigated based on copper deposition in a copper sulfate-sulfuric acid system was performed and satisfactory agreement was obtained between expermental and theoretical current distribution. The current distribution of copper deposition is secondary current distribution within the experimental conditions. Dimensionless variables, N and J as well as Wagner number were used to determine the criteria for the uniformity of current distribution.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.689-694
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• 2003

An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported pipe conveying fluid subject to the moving mass. The equation of motion is derived by using Lagrange's equation. The influences of the velocity of moving mass and the velocity of fluid flow and a crack have been studied on the dynamic behavior of a simply supported pipe system by numerical method. The presence of crack results in higher deflections of pipe. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. Totally, as the velocity of fluid flow and the crack severity are increased, the mid-span deflection of simply supported pipe conveying fluid is increased. The time which produce the maximum dynamic deflection of the simply supported pipe is delayed according to the increment of the crack severity.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.5 no.2
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• pp.84-90
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• 1993

Iterative solution procedure (Conjugate Gradient Method, Panchang et al., 1991) is implemented for solving the complete mild slope equation for the spherical shoal and the coast with detached breakwater. The numerical results agreed well with the experimental data. The disadvantage that mild slope eguation could be solved only for small domains is now overcome by using this solution procedure. Moreover it can be easily applied to the coastal regions with complex geometry and structures, and needs not so much computer time as the conventional models.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.601-606
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• 1999

A Walsh function method is proposed in this report for the analysis and optimal control of linear time-delay systems, which is based on the Picard's iterative approximation and fast Walsh transformation. In this research, the following results are obtained: 1) The differential and integral equation can be solved by transforming into a simple algebraic equation as it was possible with the usual orthogonal function method: 2) General orthogonal function methods require usage of Walsh operational matrices for delay or advance and many calculations of inverse matrices, which are not necessary in this method. Thus, the control problems of linear time-delay systems can be solved much faster and readily.

• Journal of Electrical Engineering and Technology
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• v.9 no.4
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• pp.1360-1364
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• 2014

In this paper, RCS characteristics on defect pattern of crossed dipole slot FSS having a finite size have been analyzed. To analyze RCS, we applied the electric field integral equation analysis which applies BiCGSTab algorithm with iterative method and uses RWG basis function. To verify the validity of this paper, RCS of PEC sphere has been compared to the theoretical results and FSSs with defect patterns are fabricated and measured. As defect patterns in FSS, missing one column, missing some elements, and discontinuity in surfaces are simulated and compared with the measurement results. Resonant frequency shifts in pass band and changes in bandwidth are observed. From the results, precisely predicting and designing frequency characteristics over defect patterns are essential when applying FSS structures such as FSS radomes.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.289-298
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• 2010

In this paper, we propose a second-order prediction/correction (SPC) domain decomposition method for solving one dimensional linear hyperbolic partial differential equation $u_{tt}+a(x,t)u_t+b(x,t)u=c(x,t)u_{xx}+{\int}(x,t)$. The method can be applied to variable coefficients problems and singular problems. Unconditional stability and error analysis of the method have been carried out. Numerical results support stability and efficiency of the method.