• 대한수학회논문집
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• 제37권3호
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• pp.939-955
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• 2022

In this paper, we study a first-order non-linear singularly perturbed Volterra integro-differential equation (SPVIDE). We discretize the problem by a uniform difference scheme on a Bakhvalov-Shishkin mesh. The scheme is constructed by the method of integral identities with exponential basis functions and integral terms are handled with interpolating quadrature rules with remainder terms. An effective quasi-linearization technique is employed for the algorithm. We establish the error estimates and demonstrate that the scheme on Bakhvalov-Shishkin mesh is O(N^-1) uniformly convergent, where N is the mesh parameter. The numerical results on a couple of examples are also provided to confirm the theoretical analysis.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2009년도 정기 학술대회
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• pp.534-535
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• 2009

This paper deals with BEM analysis of transient elastodynamic problems using domain decomposition method and particular integrals. The particular method is used to approximate the acceleration term in the governing equation. The domain decomposition method is examined to consider multi-region problems. The domain of the original problem is subdivided into sub-regions, which are modeled by the particular integral BEM. The iterative coupling employing Schwarz algorithm is used for the successive update of the interface boundary conditions until convergence is achieved. The numerical results, compared with those by ABAQUS, demonstrate the validity of the present formulation.

• 한국광학회:학술대회논문집
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• 한국광학회 1990년도 제5회 파동 및 레이저 학술발표회 5th Conference on Waves and lasers 논문집 - 한국광학회
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• pp.64-68
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• 1990

Boundary element method using linear basis function is applied to obtain fields scattered from a 3-D dielectric sphere. Electric field integral equation is used on the surfaces of the dielectric material where its surface is discretized into trilateral cells. For plane wave incidence, scattered fields by a dielectric sphere is calculated and compared with its analytic solution. The total electric fields are calculated on the great circle of the sphere boundary as well as the outside of the sphere in the plane of the wave vector and the polarization vector of the incident electric field.

• 한국정밀공학회지
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• 제19권5호
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• pp.81-88
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• 2002

An interface crack of a piezoelectric medium bonded between an elastic layer and a half-space is analyzed using the theory of linear piezoelectricity. Both out-of-plane mechanical and in-plane electrical loads are applied to the piezoelectric laminate. By the use of courier transforms, the mixed boundary value problem is reduced to a singular integral equation which is solved numerically to determine the stress intensity factors. Numerical analyses for various material combinations are performed and the results are discussed.

• 한국생산제조학회지
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• 제20권4호
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• pp.464-471
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• 2011

We tried to analyze sound field of the interior of housing installed with an impeller using the Boundary Element Method (BEM) with the Kirchhoff-Helmholtz integral equation. In order to increase the accuracy of our analysis, reverse engineering technology, which has been developed in recent years. We measured and treated geometrical data with 3D scanning of the practical research object. After modeling by the reverse engineering, we analyzed variation of the BPF as adding vibration frequency and variation of the sound field of the interior of housing by changing the number of impeller blades. We also tried an analysis of free degree variation. Then, we proposed the analysis accuracy and noise reducing method by analysis result.

• International Journal of Aeronautical and Space Sciences
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• 제3권2호
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• pp.76-81
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• 2002

A numerical simulation of wake behavior behind three-dimensional wings in ground effect is done using an indirect boundary element method (Panel Method). An integral equation is obtained by applying Green's 2nd Identity on all surfaces of the flow domain. The AIC is constructed by imposing the no penetration condition on solid surfaces, and the Kutta at the wing's trailing edge. The ground effect is included using an image method. At each time step, a row of wake panels from wings' trailing edge are convected downstream following the force-free condition. The roll-up of wake vortices behind wings in close proximity is simulated.

• International Journal of Aeronautical and Space Sciences
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• 제3권2호
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• pp.82-87
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• 2002

Aerodynamic analysis of NACA wings moving with a constant speed over guideways are performed using an indirect boundary element method (potential-based panel method). An integral equation is obtained by applying Green's theorem on all surfaces of the fluid domain. The surfaces over the wing and the guideways are discretized as rectangular panel elements. Constant strength singularities are distributed over the panel elements. The viscous shear layer behind the wing is represented by constant strength dipoles. The unknown strengths of potentials are determined by inverting the aerodynamic influence coefficient matrices constructed by using the no penetration conditions on the surfaces and the Kutta condition at the trailing edge of the wing. The aerodynamic characteristics for the wings flying over nonplanar ground surfaces are investigated for several ground heights.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 1997년도 춘계 학술발표회 논문집 Proceedings of EESK Conference-Fall 1997
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• pp.128-135
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• 1997

The indirect boundary integral equation is formulated to analyze the behavior of a cavity in a multilayered half-plane subjected to earthquake waves. This formulation uses the fundamental solutions that are numerically calculated by the generalized transmission and reflection coefficient method. The free surface of the cavity without external excitation influences the behavior of the half-plane. Consequently this analysis adds the consideration of scattering-field into the analysis and the total motion field of the cavity is decomposed into the free-field and scattering-field motions. The free-field motion is obtained from the modification of the transmission and reflection coefficient method. The scattering-field motion is calculated is calculated by the indirect boundary value problem which has the ficticious boundaries and sources. In this study, P wave, SV wave, SH wave, and Rayleigh wave are analyzed respectively.

• 전자공학회논문지B
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• 제29B권3호
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• pp.6-15
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• 1992

This paper proposes a method for the global optimization of redundancy over the whole task period for a kinematically redundant robot. The necessary conditions based on the calculus of variations for an integral type cost criterion result in a second-order differential equation. For a cyclic task, the periodic boundary conditions due to conservativity requirements are discussed. We refine the two-point boundary value problem to an initial value adjustment problem and suggest a numerical search method for providing the conservative global optimal solution using the gradient projection method. Since the initial joint velocity is parameterized with the number of the redundancy, we only search the parameter value in the space of as many dimensions as the number of degrees of redundancy. We show through numerical examples that multiple nonhomotopic extremal solutions and the generality of the proposed method by considering the dynamics of a robot.

• Journal of the Korean Physical Society
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• 제80권
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• pp.30-36
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• 2022

Holographic model of massive scalar field with its self-interaction λϕⁿ in AdS space is able to give a logarithmic scale dependence to marginal multi-trace deformation couplings on its dual conformal field theory, where λ is the self-interaction coupling of the scalar field, ϕ, and n is an integral number. In arXiv:1501.06664, the authors realize this feature by looking at bulk scalar solutions near AdS boundary imposing a specific boundary condition between the coefficients of non-normalizable and normalizable modes of the scalar field excitations. We study the same holographic model to see scale dependence of marginal deformations on the dual conformal field theory by employing completely different method: holographic Wilsonian renormalization group. We solve Hamilton-Jacobi equation derived from the holographic model of massive scalar with λϕⁿ interaction and obtain the solution of marginal multi-trace deformations up to the leading order in λ. It turns out that the solution of marginal multi-trace deformation also presents logarithmic behavior in energy scale near UV region.