• Geophysics and Geophysical Exploration
• /
• v.21 no.1
• /
• pp.1-7
• /
• 2018

In the two-dimensional (2D) modeling of electrical method, the potential in the space domain is reconstructed with the calculated potentials in the wavenumber domain using inverse Fourier transform. The inverse Fourier integral is numerically evaluated using the transformed potential at different wavenumbers. In order to improve the precision of the integration, either the logarithmic or exponential approximation has been used depending on the size of wavenumber. Two numerical methods have been generally used to evaluate the integral; interval integration and Gaussian quadrature. However, both methods do not consider the distance from the current source. Thus the resulting potential in the space domain shows some error. Especially when the distance from the current source is very small or large, the error increases abruptly and the evaluated potential becomes extremely unstable. In this study, we developed a new method to calculate the integral accurately by introducing the distance from the current source to the rescaled Gauss abscissa and weight. The numerical tests for homogeneous half-space model show that the developed method can yield the error level lower than 0.4 percent over the various distances from the current source.

• Communications of Mathematical Education
• /
• v.26 no.2
• /
• pp.155-176
• /
• 2012

In this paper, we present a practical and essential method of using team projects for calculus. We, specifically, take into account the team project that calculate the volume of lung represented on CT scan images. We have demonstrated that the process of analyzing the images in a team project encourage studying numerical methods of integration for calculus. Also, we have used various technological programs(MATLAB, MATHEMATICA, MS Excel) to solve the team project.

• Journal of the Korea Institute of Military Science and Technology
• /
• v.5 no.4
• /
• pp.57-66
• /
• 2002

본 연구는 굽힘 하중하에서 탄성평판 구조 해석을 위한 경계적분방법 구성을 주목적으로 하고 체계적인 모듈화시스템 개발의 첫 이론 부분을 확립하였다. 굽힘 문제에서의 4개의 고유변수인 처짐, 기울기, 굽힘모우멘트, 상당 전단력의 항으로 경계적분방정식을 구성하였다. 물리적인 의미를 갖는 두 새로운 핵함수 도입으로 구성된 이들 적분방정식은 경계요소 구성시 나타나는 특이거동의 문제점을 간단한 두 탄성해에 의해 정규화 시켰으며 수치 적분 과정도 Cauchy 주치 적분 수렴성에서의 특별취급과는 달리 효율적으로 일반화시켰다. 경계적분식의 수치해석방법을 서술하였으며 집중하중하의 비대칭문제의 근사수치해를 도시하였다.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.31 no.7
• /
• pp.1-8
• /
• 2003

Numerical characteristics of air chemistry associated with hypersonic flows are described and are compared with those of hydrogen oxygen combustion, applying the partially implicit time integration method to air chemistry. This paper reveals that the time integration of air chemistry needs a chemical Jacobian for stable calculations. However the positive real eigenvalues in air chemistry are relatively smaller than those of hydrogen combustion, and the numerical integration is less sensitive than that with combustion. lt is also found that the application of the partia1ly irnplicit method reduces the computing time without numerical instabilities.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.27 no.4
• /
• pp.437-444
• /
• 2009

A bi-directional, multi-step numerical integrator is developed to determine the GPS (Global Positioning System) orbit based on a dynamic approach, which shows micrometer-level accuracy at GPS altitude. The acceleration due to the planets other than the Moon and the Sun is so small that it is replaced by the empirical forces in the Solar Radiation Pressure (SRP) model. The satellite orbit parameters are estimated with the least-squares adjustment method using both the integrated orbit and the published IGS (International GNSS Service) precise orbit. For this estimation procedure, the integration should be applied to the partial derivatives of the acceleration with respect to the unknown parameters as well as the acceleration itself. The accuracy of the satellite orbit is evaluated by the RMS (Root Mean Squares error) of the residuals calculated from the estimated orbit parameters. The overall RMS of orbit error during March 2009 was 5.2 mm, and there are no specific patterns in the absolute orbit error depending on the satellite types and the directions of coordinate frame. The SRP model used in this study includes only the direct and once-per-revolution terms. Therefore there is errant behavior regarding twice-per-revolution, which needs further investigation.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.7 no.1
• /
• pp.96-102
• /
• 1983

복사 형상계수를 계산하는 새롭고도 간단한 수치적 방법이 개발되었다. 유한선분 적분법은 윤 곽적분을 이용하며, 윤곽은 유한한 수의 선분으로 구성된 것으로 가정한다. 미소면적으로부터 유한면적까지의 복사 형상계수는 적분로 상의 절점의 좌표값에만 관계되며, 전자 계산기에 쉽게 프로그램 될 수 있다. 가우스의 적분을 이용하여 두 유한 면적사이의 복사 형상계수를 구한다. 미소 면적에서 원판까지, 두 개의 평행원판 사이, 및 두 개의 직사각형 사이의 복사 형상계수를 구하여 엄밀해와 비교하여 유한선분 적분법의 정확성이 우수함을 보였다. 단위구와 단위 정사 각형에서 타원체까지의 보가 형상계수의 값도 구하였다.

• Journal of the Society of Naval Architects of Korea
• /
• v.29 no.1
• /
• pp.43-54
• /
• 1992

A method of evaluating the velocity components induced by a Havelock source is presented in this paper. The mathematical manipulation of x, y and z-derivative of the Green function of the Havelock source by the use of contour integration on the complex plane has resulted in the expressions that can be readily incorporated with computer program. The accuracy and efficiency that can be secured by the use of the present mathematical expressions have been convincingly found to be highly satisfactory.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2022.05a
• /
• pp.248-248
• /
• 2022

Hwang(2015)은 불연속 지형을 지나는 천수 흐름의 수치 해석에서 불연속 전면에 의한 추력(thrust)에 주목하여 그 영향을 흐름률(flux) 계산에 반영하는 새로운 기법을 제시하였다. 이 기법 덕분에 수심 적분 모형으로도 계단이나 보와 같이 직립한 하천 구조물의 불연속면을 경사로 완화하지 않고 직접 모의할 수 있다. 직립 측면 위어 실험에 Hwang(2015)의 기법이 적용됨으로써 연직면을 경사면으로 완화하여야 하는 기존의 수심 적분 모형에 비해 계산 격자 개수가 53%로 줄었다(Hwang, 2019). Hwang(2019)은 기존 모형과 비교를 통해, 정확도를 어느 정도 유지하면서도, 소요된 계산 시간이 20%에 불과하다고 주장하였다. 여기에서는 보다 다양한 직립 광정 위어 실험에 적용하여 수심 적분 모형에 의한 월류량을 검토하고자 한다.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.14 no.6
• /
• pp.1408-1416
• /
• 1990

A powerful and efficient method for finding approximate solutions to initial-boundary-value problems in the transient coupled thermoelasticity is formulated in time domain using the finite element technique with time-marching strategy. The final system equations can be derived by the Guritin's variational principle using the definition of convolution integral. But, the finite element formulation for the equations of motion is modified by differentiating in time. Numerical results to some test problems are compared with analytical and other sophisticated approximate solutions. Stable responces are observed in all the given examples irrespective of incremental time steps and mesh shapes. In addition, it is shown that good numerical results are obtained even in coarser mesh or larger time step comparing to other numerical methods.

• Journal of Digital Convergence
• /
• v.19 no.12
• /
• pp.339-345
• /
• 2021

In this paper, estimation angle performance analysis of amplitude-comparison monopulse radar under additive noise effect is dealt with. When uncorrelated white noises are added to the squinted beams, the angle estimation performance is analyzed through the mean square error(MSE). The numerical integration-based mean square error result completely overlaps the Monte Carlo-based mean square error result, which corresponds to 99.8% of the Monte Carlo-based mean square error result. In addition, the mean square error analysis method based on numerical integration has a much faster operation time than the mean square error method based on Monte Carlo. the angle estimation performance of the amplitude comparison monopulse radar can be efficiently analyzed in various noise environments through the proposed numerical integration-based mean square error method.