• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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• pp.337-350
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• 2014

In this paper, we consider discontinuous Galerkin finite element methods with interior penalty term to approximate the solution of nonlinear parabolic problems with mixed boundary conditions. We construct the finite element spaces of the piecewise polynomials on which we define fully discrete discontinuous Galerkin approximations using the Crank-Nicolson method. To analyze the error estimates, we construct an appropriate projection which allows us to obtain the optimal order of a priori ${\ell}^{\infty}(L^2)$ error estimates of discontinuous Galerkin approximations in both spatial and temporal directions.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1017-1029
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• 2019

In this paper, blows-up and global solutions for a class of nonlinear divergence form parabolic equations with the abstract form of $({\varrho}(u))_t$ and time dependent coefficients are considered. The conditions are established for the existence of a solution globally and also the conditions are established for the blow up of the solution at some finite time. Moreover, the lower bound and upper bound of the blow-up time are derived if blow-up occurs.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.10 no.5
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• pp.237-244
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• 2010

In this paper, the dual parabolic cylindrical reflector systems are analyzed as the reflector system for the CATR(Compact Antenna Test Range) facility. The near-field at the test zone of the CATR is calculated by using the PO(Physical Optics) approximation. The CATR has to provide an uniform plane wave with the minimum amplitude and phase ripple and the low cross polarization. Therefore, in this paper, the near-field pattern are calculated, and the ripple and taper of the field and the cross polarization are investigated with the position of the subreflector and the test region. It is confirmed that the analysis results can be used for the design of the CATR with the dual parabolic cylindrical reflector.

• 한국신재생에너지학회:학술대회논문집
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• 2006.11a
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• pp.165-167
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• 2006

On our return to India from Germany, we have worked on the development of parabolic solar concentrators with input and collaboration of German and Austrian inventors. We have gradually improved the solar technologies to include food processing based on inputs and feedback from users to fulfill their specific requirements. We will discuss the acceptability and commercialisation of various systems that we have successfully developed, their implications and their benefit. These success stories can work as multipliers. These concentrators can have various other applications. The Global Treaty Kyoto Protocol's CDM (Clean Development Mechanism) can result in a win-win situation for both developing and developed nations and the world environment at large - whereby developed nations get carbon credits by supporting renewable energy projects in developing nations. North-South dialogue and South-South dialogue can effectively foster global co-operation meaningfully to benefit People and environments ensuring sustainable development and protection of Our planet Earth, our only HOME!!!

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.2
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• pp.230-236
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• 2011

This paper proposes the possibility which the fuzzy theory can be used to improve the performance of the parabolic SAR(Stop-And-Reverse) indicator in the trading systems for stock market. The simulation results with data of the KOSPI 200 future show that the occurred number of trading signals and the false signals in the proposed fuzzy SAR indicator is less than that in the conventional SAR indicator. In the conventional SAR system, the incremental value of the acceleration factor is usually setted as 0.02 and the maximum value of the acceleration factor is usually limited as 0.2. But in the proposed fuzzy SAR system, the incremental value and the maximum value of the acceleration factor are automatically adjusted by using the fuzzy rules, which are designed based-on the difference between short-term moving average and medium-term moving average and also based-on the slope of short-term moving average.

• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.75-90
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• 2015

In this paper the existence of global solutions of the parabolic cross-diffusion systems with cooperative reactions is obtained under certain conditions. The uniform boundedness of $W_{1,2}$ norms of the local maximal solution is obtained by using interpolation inequalities and comparison results on differential inequalities.

• The Journal of the Acoustical Society of Korea
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• v.39 no.1
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• pp.1-7
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• 2020

The acoustic parabolic equation method in the ocean is an efficient technique to calculate the acoustic field in the range-dependent environment, emanating from a point source. However, we often need to use the directional source with a main beam in the practical problem. In this paper, we present two methods to implement the directional source in the acoustic parabolic equation code easily. One is simply to filter the Delta function idealized as an omni-directional point source. Another method is based on the rational filtering of the self-starter solution. It has a limitation not to separate the up-going and the down-going wave for the depth, but would be useful in implementing the mode propagation. Numerical examples for validation are given in the Pekeris environment and the deep sea environment.

• The Journal of the Acoustical Society of Korea
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• v.36 no.1
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• pp.1-11
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• 2017

In this study, novel approximate form of the square-root operator of three dimensional acoustic Parabolic Equation (3D PE) is proposed using a rational approximant for two variables. This form has two advantages in comparison with existing approximation studies of the square-root operator. One is the wide-angle capability. The proposed form has wider angle accuracy to the inclination angle of ${\pm}62^{\circ}$ from the range axis of 3D PE at the bearing angle of $45^{\circ}$, which is approximately three times the angle limit of the existing 3D PE algorithm. Another is that the denominator of our approximate form can be expressed into the product of one-dimensional operators for depth and cross-range. Such a splitting form is very preferable in the numerical analysis in that the 3D PE can be easily transformed into the tridiagonal matrix equation. To confirm the capability of the proposed approximate form, comparative study of other approximation methods is conducted based on the phase error analysis, and the proposed method shows best performance.

• Journal of Mechanical Science and Technology
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• v.16 no.10
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• pp.1264-1275
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• 2002

This paper is concerned with the investigation on the stability and convergence characteristics of the Crank-Nicolson-Galerkin scheme that is widely being employed for the numerical approximation of parabolic-type partial differential equations. Here, we present the theoretical analysis on its consistency and convergence, and we carry out the numerical experiments to examine the effect of the time-step size △t on the h- and P-convergence rates for various mesh sizes h and approximation orders P. We observed that the optimal convergence rates are achieved only when △t, h and P are chosen such that the total error is not affected by the oscillation behavior. In such case, △t is in linear relation with DOF, and furthermore its size depends on the singularity intensity of problems.

• ETRI Journal
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• v.29 no.6
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• pp.817-819
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• 2007

A low-stress organic polymer membrane is proposed as a deformable mirror that can be incorporated into a cellular phone camera to achieve auto focusing without motor-type moving parts. It is demonstrated that our fabricated device has an optical power of 20 diopters and can switch focus in 14 ms. The surface roughness of the organic membrane is measured around 15 nm, less than ${\lambda}$/20 of the visible light. With curve fitting, we found that the actuated membrane is almost parabolic in shape, which leads to less aberration than spherical surfaces. It is suitable for reflective-optics systems.