• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 2008년도 정기 학술대회
• /
• pp.39-44
• /
• 2008

Stress wave propagation plays an important role in many engineering problems for reducing industrial noise and vibrations. In this paper, the dispersion-corrected finite element model is proposed for reducing the dispersion error in simulation of stress wave propagation. At eliminating the numerical dispersion error arising from the numerical simulation of stress wave propagation, numerical dispersion characteristics of the wave equation based finite element model are analyzed and some dispersion control scheme are proposed. The validity of the dispersion correction techniques is demonstrated by comparing the numerical solutions obtained using the present techniques.

• 한국해양공학회지
• /
• 제12권2호통권28호
• /
• pp.97-110
• /
• 1998

The numerical damping and dispersion error characteristics associated with difference schemes and a panel shift method used for the calculation of steady free surface flows by a panel method are an analysed in this paper. First, 12 finite difference operators used for the double model flow by Letcher are applied to a two dimensional cylinder with the Kelvin free surface condition and the numerical errors with these schemes are compared with those by the panel shift method. Then, 3-D waves due to a submerged source are calculated by the difference schemes, the panel shift method and also by a higher order boundary element method(HOBEM). Finally, the waves and wave resistance for Wigley's hull are calculated with these three schemes. It is shown that the panel shift method is free of numerical damping and dispersion error and performs better than the difference schemes. However, it can be concluded that the HOBEM also free of the numerical damping and dispersion error is the most stable, accurate and efficient.

• Journal of electromagnetic engineering and science
• /
• 제8권4호
• /
• pp.139-143
• /
• 2008

In this paper, a new scheme to calculate the weighting factor of the 2-D isotropic-dispersion finite difference time domain(ID-FDTD) is proposed. The weighting factor in [1] was formulated in free space, so that it may not be optimal in dielectric media. Therefore, the weighting factor was reformulated by considering the material properties and using the least mean square method. As a result, a minimum numerical dispersion error for any dielectric media is guaranteed.

• 한국전산구조공학회논문집
• /
• 제17권1호
• /
• pp.75-82
• /
• 2004

본 논문에서는 응력파 전파를 수치모의할 때 발생하는 수치적인 분산효과를 제거하기 위해 파동방정식에 기초한 일차원 유한요소모형을 이용하여 수치분산오차의 특성을 분석하고 분산오차를 제어할 수 있는 방법을 제안하였다. 질량행렬을 그대로 사용하는 경우와 집중질량행렬을 사용하는 경우에 대한 수치분산오차를 분석하였다. 개발된 분산제어기법은 공간미분항의 시간단계 가중치 및 질량집중도를 조정하는 음해법과 인위적인 분산항을 추가하는 양해법의 두가지 방법이다. 제안된 분산보정기법을 이용하여 계산한 수치해와 파동방정식의 해석해를 비교한 결과 본 연구에서 제안한 분산보정기법의 타당성을 확인하였다.

• 대한수학회보
• /
• 제47권6호
• /
• pp.1225-1234
• /
• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

• Journal of electromagnetic engineering and science
• /
• 제13권3호
• /
• pp.158-164
• /
• 2013

This paper expands a previously proposed optimized higher order (2, 4) finite-difference time-domain scheme (H(2, 4) scheme) for use with lossy material. A low dispersion error is obtained by introducing a weighting factor and two scaling factors. The weighting factor creates isotropic dispersion, and the two scaling factors dramatically reduce the numerical dispersion error at an operating frequency. In addition, the results confirm that the proposed scheme performs better than the H(2, 4) scheme for wideband analysis. Lastly, the validity of the proposed scheme is verified by calculating a scattering problem of a lossy circular dielectric cylinder.

• 한국대기환경학회지
• /
• 제13권5호
• /
• pp.383-396
• /
• 1997

Numerical prediction of the pollutant dispersion over a two-dimensional hilly terrain is presented. The dispersion model used in the present work is based on the gradient diffusion theory and the finite-volume method on a non-orthogonal boundary-fitted grid system. The numerical model is validated by comparing the results with the available experimental data for the flat-floor dispersion within a turbulent boundary-layer. The numerical error analysis is performed based on the guideline of Kasibhatla et al.(1988) for the elevated-source dispersion in the flat-floor boundary layer having a power-law velocity and linear eddy-diffusivity profile. The influences of the two-dimensional hilly terrain on the dispersion from a continuously released source are numerically investigated by changing the emission locations and heights. It is found that the distributions of ground-level concentration are strongly influenced by the source location and the emission height. Hence, the terrain amplification factor is greatly enhanced when the pollutant source is located within a flow separation region. Dispersion from a source of short duration is also simulated and the duration time of the pollutant is compared at several downstream locations on a hilly terrain. The results of the numerical prediction are applied to the evaluation of environmental impacts due to the automobile exhausts at the seashore highway with a parallel mountain range.

• 한국전자파학회논문지
• /
• 제29권3호
• /
• pp.225-232
• /
• 2018

본 논문은 H(2,4) 기법을 기반으로 한 저분산 유한차분 시간영역법(Finite-Difference Time-Domain: FDTD)을 이용하여 상수 도전율과 비유전율을 갖는 유전체의 광대역 전자기 특성을 정확하게 해석하는 방법을 제안했다. 수치분산오차를 최소화하기 위해서 제안한 FDTD 기법에서 이용하는 세 개의 변수의 최적값을 계산하였다. 잘 알려진 정확한 FDTD 기법들과 제안한 FDTD 방법으로 2차원 원형 유전체 실린더의 광대역 산란 문제를 계산하였고, 그 결과를 이론값과 비교하여 제안한 방법의 우수성을 검증하였다.

• 한국전자파학회논문지
• /
• 제21권7호
• /
• pp.805-814
• /
• 2010

기존 Crank-Nicolson FDTD 기법(CN FDTD 기법)의 비등방성 분산 특성을 개선하기 위한 CN ID-FDTD 기법을 제안하였다. 제안한 CN ID-FDTD 기법은 공간 미분 연산을 위해 기존 CN FDTD 기법의 centered 유한 차분식 (Finite Difference equation: FD 연산식)이 아닌 isotropic-dispersion 유한 차분식(ID-FD 연산식)$^{[1],[2]}$을 이용한다. 본 논문에서는 손실 매질에 대한 CN ID-FDTD 기법의 분산 관계식을 유도하였고, 이 분산 관계식을 이용해 ID-FD 연산식에서 분산 오차(dispersion error)를 줄이는 가중치(weighting factor)와 보정값(scaling factor)을 제시하였다. 그리고 해석 결과의 정확성 비교를 통해 CN ID-FDTD 기법에서는 기존 CN FDTD 기법의 단점이었던 비등방성 분산 오차가 확연하게 감소하는 것을 확인하였다.

• Structural Engineering and Mechanics
• /
• 제74권4호
• /
• pp.547-557
• /
• 2020

In this paper, an automatic adaptive mesh refinement procedure is presented for two-dimensional problems on the basis of a new probabilistic error estimator. First-order perturbation theory is employed to determine the lower and upper bounds of the structural displacements and stresses considering uncertainties in geometric sizes, material properties and loading conditions. A new probabilistic error estimator is proposed to reduce the mesh dependency of the responses dispersion. The suggested error estimator neglects the refinement at the critical points with stress concentration. Therefore, the proposed strategy is combined with the classic adaptive mesh refinement to achieve an optimal mesh refined properly in regions with either high gradients or high dispersion of the responses. Several numerical examples are illustrated to demonstrate the efficiency, accuracy and robustness of the proposed computational algorithm and the results are compared with the classic adaptive mesh refinement strategy described in the literature.