• Kyungpook Mathematical Journal
• /
• 제60권4호
• /
• pp.869-881
• /
• 2020

Most first kind integral equations are ill-posed, and obtaining their numerical solution often requires solving a linear system of algebraic equations of large condition number, which may be difficult or impossible. This article proposes a regularization-direct method to numerically solve first kind Fredholm integral equations. The vector forms of block-pulse functions and related properties are applied to formulate the direct method and reduce the integral equation to a linear system of algebraic equations. We include a regularization scheme to overcome the ill-posedness of integral equation and obtain a stable numerical solution. Some test problems are solved using the proposed regularization-direct method to illustrate its efficiency for solving first kind Fredholm integral equations.

• 한국음향학회지
• /
• 제7권4호
• /
• pp.22-30
• /
• 1988

이 논문에서는 무한 격리벽내의 가장자리가 고정된 원형평판으로부터의 음압복사를 FFT 기법을 이용하여 계산하였다. 음장은 컴퓨터 계산시간을 절약하기 위해 Rayleigh integral 을 직접 수치해석적으로 구하는 대신에 공간영역에서 2차원 FFT 방법을 이용하였다. 그 결과 1/200의 시간을 절약할 수 있었다. FET방법은 원형평판형상 뿐만아니라 어떤 형상에도 적용 가능하며 복잡한 형상의 근거리 및 원거리 음장을 예측하는데 상당히 유효하다.

• Journal of Electrical Engineering and information Science
• /
• 제1권1호
• /
• pp.58-69
• /
• 1996

This paper presents a new approach to derive an energy integral based on an Equivalent Mechanical Model(EMM), which is developed by introducing imaginary springs for line resistances. The proposed EMM shows that phasor currents and voltages are directly analogous to the two-dimensional force and displacement vectors, respectively. Through rigorous energy analysis of the proposed EMM, an exact energy integral expression is derived for multimachine systems, and several useful theorems are developed to derive an energy integral for power systems with detailed generator models the energy integral exactly reflects the internal resistance, saliency and flux-decaying effects of the generator. Finally, an illustrative example is given for a multimachine system adopting the Eq'-model for generators, which shows that the consideration of a detailed generator model does not aggravate the complicacy of the direct method of stability analysis in multimachine systems.

• 대한조선학회지
• /
• 제24권4호
• /
• pp.19-36
• /
• 1987

In this research the coupling problem between the elastic structure and the fluid, specially the hydroelastic harmonic vibration problem, is studied. In order to couple the domains, i.e., the structural domain and the fluid domain, the boundary integral method(direct boundary integral formulation) is used in the fluid domain in combination with the finite element method for the structure. The boundary integral method has been widely developed to apply it to the hydroelastic vibration problem. The hybrid boundary integral method using eigenfunctions on the radiation boundaries and the boundary integral method using the series form image-functions to replace the even bottom and free surface boundaries in case of high frequencies have been developed and tested. According to the boundary conditions and the frequency ranges the different boundary integral methods with the different idealizations of the fluid boundaries have been studied. Using the same interpolation functions for the pressure distribution and the displacement the two domains have been coupled and using Hamilton principle the solution of the hydroelastic have been obtained through the direct minimizing process. It has become evident that the finite-boundary element method combining with the eigenfunction or the image-function method give good results in comparison with the experimental ones and the other numerical results by the finite element method.

• 소음진동
• /
• 제7권6호
• /
• pp.975-984
• /
• 1997

A direct boundary element method (DBEM) is developed for thin bodies whose surfaces are rigid or compliant. The Helmholtz integral equation and its normal derivative integral equation are adoped simultaneously to calculate the pressure on both sides of the thin body, instead of the jump values across it, to account for the different surface conditions of each side. Unlike the usual assumption, the normal velocity is assumed to be discontinuous across the thin body. In this approach, only the neutral surface of the thin body has to be discretized. The method is validated by comparison with analytic and/or numerical results for acoustic scattering and radiation from several surface conditions of the thin body; the surfaces are rigid when stationary or vibrating, and part of the interior surface is lined with a sound-absoring material.

• 산업기술연구
• /
• 제20권A호
• /
• pp.203-209
• /
• 2000

The fluctuation integrals which give useful information in the structure of solution are associated with the mixed direct correlation integral ($C_{12}$) known. Using its weighted arithmetic mean of $C_{11}$ and $C_{22}$ and the activity coefficient model, the fluctuation integrals on solute-solute, solvent-solute, and solvent-solvent can be calculated in the function of mole fraction. In this work, several binary mixtures containing c-hexane were tested and the results on the fluctuation integrals were rather good.

• 충청수학회지
• /
• 제10권1호
• /
• pp.37-41
• /
• 1997

In this paper, we give a direct proof that the Perron and variational integrals are equivalent.

• Korean Journal of Mathematics
• /
• 제18권4호
• /
• pp.425-440
• /
• 2010

Using Green's theorem, elliptic boundary value problems can be converted to boundary integral equations. A numerical methods for boundary integral equations are boundary elementary method(BEM). BEM has advantages over finite element method(FEM) whenever the fundamental solutions are known. Helmholtz type equations arise naturally in many physical applications. In a boundary integral formulation for the exterior Neumann there occurs a hypersingular operator which exhibits a strong singularity like $\frac{1}{|x-y|^3}$ and hence is not an integrable function. In this paper we are going to remove this hypersingularity by reducing the regularity of test functions.

• 대한수학회보
• /
• 제60권6호
• /
• pp.1439-1451
• /
• 2023

This paper provides a constructive proof of the weak factorizations of the classical Hardy space H¹(ℝⁿ) in terms of multilinear fractional integral operator on the variable Lebesgue spaces, which the result is new even in the linear case. As a direct application, we obtain a new proof of the characterization of BMO(ℝⁿ) via the boundedness of commutators of the multilinear fractional integral operator on the variable Lebesgue spaces.

• 대한전자공학회논문지
• /
• 제23권4호
• /
• pp.445-449
• /
• 1986

This paper presents a direct adaptive control scheme for nonminimum phase systems of which controller parameters are estimated from the least-squares algorithm, and some additional auxiliadry parameters are obtianed from the proposed polynomial identity equation. Integral action is incorporated into the adaptive controller to eliminate the steady-state error, and to satisfy a condition of the unique solution for the polynomial identity as well.