• Coupled systems mechanics
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• 제1권2호
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• pp.183-204
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• 2012

A method for the analysis of wave scattering in 3-D elastic full space is developed by means of the coupled boundary-volume integral equation, which takes into account the effects of both the boundary of inclusions and the uctuation of the wave field. The wavenumber domain formulation is used to construct the Krylov subspace by means of FFT. In order to achieve the wavenumber domain formulation, the boundary-volume integral equation is transformed into the volume integral equation. The formulation is also focused on this transform and its numerical implementation. Several numerical results clarify the accuracy and effectiveness of the present method for scattering analysis.

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

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.1078-1082
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• 2001

An alternative formulation of the Helmholtz integral equation is derived to express the pressure field explicitly in terms of the velocity vector of a radiating surface. This formulation, derived for arbitrary sources, is similar in form to the Rayleigh's formula for planar sources. Because the pressure field is expressed explicitly as a surface integral of the particle velocity, which can be implemented numerically using standard Gaussian quadratures, there is no need to use Boundary element method to solve a set of simultaneous equations for the surface pressure at the discretized nodes. Furthermore the non-uniqueness problem inherent in methods based on Helmholtz integral equation is avoided. Validation of this formulation is demonstrated for some simple geometries.

• 한국음향학회지
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• 제27권8호
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• pp.411-417
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• 2008

본 논문에서는 헬름홀쯔 적분 방정식에서 유도된 식을 이용하여 구조물의 표면 압력을 구조진동 성분에 대한 단순한 적분형태로 표현하여 음향방사 및 구조/음향 연성 문제를 수치적으로 푸는 방법에 대하여 다룬다. 이 식은 임의의 형상에 대하여 유도된 식으로 Rayleigh 식과 유사한 형태를 갖는다. 이 식을 이용하면 표면 압력을 구조물의 속도에 대한 단순 적분 형태로 나타낼 수 있기 때문에 경계요소법과 같이 연립방정식에 대한 행렬식을 풀 필요가 없다. 또한 헬름홀쯔 적분 방정식에 기반을 둔 다른 방법 들이 가지는 해의 유일성 문제도 갖지 않는 장점이 있다. 본 논문에서는 구형 셀에 대하여 수치해와 정해를 비교하여 제안한 방법의 타당성을 검증하였다.

• 대한자원환경지질학회:학술대회논문집
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• 대한자원환경지질학회 2000년도 춘계공동학술발표회
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• pp.166-167
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• 2000

• Journal of electromagnetic engineering and science
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• 제14권3호
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• pp.273-277
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• 2014

In this research, integral transform technique for electromagnetic scattering formulation is reviewed. Electromagnetic boundary-value problems are presented to demonstrate how the integral transforms are utilized in electromagnetic propagation, antennas, and electromagnetic interference/compatibility. Various canonical structures of slotted conductors are used for illustration; moreover, Fourier transform, Hankel transform, Mellin transform, Kontorovich-Lebedev transform, and Weber transform are presented. Starting from each integral transform definition, the general procedures for solving Helmholtz's equation or Laplace's equation for the potentials in the unbounded region are reviewed. The boundary conditions of field continuity are incorporated into particular formulations. Salient features of each integral transform technique are discussed.

• 대한전기학회논문지:전기물성ㆍ응용부문C
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• 제53권12호
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• pp.626-633
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• 2004

In this paper, we present a time domain combined field integral equation (TD-CFIE) formulation to analyze the transient electromagnetic response from three-dimensional dielectric objects. The solution method in this paper is based on the method of moments (MoM) that involves separate spatial and temporal testing procedures. A set of the RWG (Rao, Wilton, Glisson) functions Is used for spatial expansion of the equivalent electric and magnetic current densities and a combination of RWG and its orthogonal component is used as spatial testing. We also investigate spatial testing procedures for the TD-CFIE to select the proper testing functions that are derived from the Laguerre polynomials. These basis functions are also used for temporal testing. Use of this temporal expansion function characterizing the time variable enables one to handle the time derivative terms in the integral equation and decouples the space-time continuum in an analytic fashion. Numerical results computed by the proposed formulation are presented and compared with the solutions of the frequency domain combined field integral equation (FD-CFIE).

• ETRI Journal
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• 제29권1호
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• pp.8-17
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• 2007

In this paper, we present a time domain combined field integral equation formulation (TD-CFIE) to analyze the transient electromagnetic response from dielectric objects. The solution method is based on the method of moments which involves separate spatial and temporal testing procedures. A set of the RWG functions is used for spatial expansion of the equivalent electric and magnetic current densities, and a combination of RWG and its orthogonal component is used for spatial testing. The time domain unknowns are approximated by a set of orthonormal basis functions derived from the Laguerre polynomials. These basis functions are also used for temporal testing. Use of this temporal expansion function characterizing the time variable makes it possible to handle the time derivative terms in the integral equation and decouples the space-time continuum in an analytic fashion. Numerical results computed by the proposed formulation are compared with the solutions of the frequency domain combined field integral equation.

• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.557-581
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• 2022

The anisotropic-diffusion convection equation with exponentially variable coefficients is discussed in this paper. Numerical solutions are found using a combined Laplace transform and boundary element method. The variable coefficients equation is usually used to model problems of functionally graded media. First the variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace-transformed equation is consequently written as a boundary integral equation which involves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method are easy to implement and accurate for solving unsteady problems of anisotropic exponentially graded media governed by the diffusion convection equation.

• Structural Engineering and Mechanics
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• 제32권3호
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• pp.407-427
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• 2009

A fundamental solution for the transient, quasi-static, plane problems of linear viscoelasticity is introduced for a specific material. An integral equation has been found for any problem as a result of dynamic reciprocal identity which is written between this fundamental solution and the problem to be solved. The formulation is valid for the first, second and mixed boundary-value problems. This integral equation has been solved by BEM and algorithm of the BEM solution is explained on a sample, mixed boundary-value problem. The forms of time-displacement curves coincide with literature while time-surface traction curves being quite different in the results. The formulation does not have any singularity. Generalized functions and the integrals of them are used in a different form.