• Structural Engineering and Mechanics
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• v.23 no.3
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• pp.263-278
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• 2006

This work presents a time-truncation scheme, based on the Lagrange interpolation polynomial, for the solution of the two-dimensional scalar wave problem by the time-domain boundary element method. The aim is to reduce the number of stored matrices, due to the convolution integral performed from the initial time to the current time, and to keep a compromise between computational economy and efficiency and the numerical accuracy. In order to verify the accuracy of the proposed formulation, three examples are presented and discussed at the end of the article.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.27 no.2
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• pp.120-124
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• 1991

An interaction of turbulent boundary layer and local roughness effects was evaluated to investigate the shear frictional coefficient in diffuser. Clauser roughness function was applied to Karman's integral equation for governing equation. The roughness of overall and local diffuser surfaces were calculated using Cole's wall and wake law and Clauser's roughness function for turbulent boundary layer characteristics. The calculating results were compared with the experimental results of other paper. It shows some significant improyements for shear frictional coefficient. Computer code was then used to confirm the behavior of local frictional coefficient along with diffuser roughness surface for some reduction of shear flow stress.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.4
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• pp.489-494
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• 2013

In analysis of power transformer loss using calculation of magnetic field, Finite element method is commonly used. When using this method, calculation of magnetic field needs the very large number of elements and the performance of common work station is not sufficient to calculate the magnetic fields. In addition, the definition of boundary conditions may arise. However, When using Integral equation method, only ferromagnetic materials need to be modeled, since the domain is infinite. All the space in which the primary and secondary sources exist is regarded as free(${\mu}={\mu}_0$).

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.4
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• pp.375-382
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• 2008

The particular integral formulation for two(2D) and three(3D) dimensional inelastic transient dynamic stress analysis is presented. The elastostatic equation is used for the complementary solution. Using the concept of global shape function, the particular integrals for displacement and traction rates are obtained to approximate acceleration of the inhomogeneous equation. The Houbolt time integration scheme is used for the time-marching process. The Newton-Raphson algorithm for plastic multiplier is used to solve the system equation. Numerical results of four example problems are given to demonstrate the validity and accuracy of the present formulation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.1032-1037
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• 2003

Although the holes on the shell case are very important fer the acoustic performance, it is difficult to solve the problem because the case includes thin bodies. Hence, in the past, only the method of trial and error, which depends on the engineer's intuition and experience, was available fur the design of holes. Many researchers have tried to solve the thin-body acoustic problems, since the conventional boundary element method (BEM ) using the Helmholtz integral equation fails to yield a reliable solution fer the numerical modelling of radiation anti scattering of sound from thin bodies. In the area of the analysis of thin-body acoustic problem, three approaches are generally used; the multi-domain BEM, the indirect variational BEM, and the normal derivative integral equation And there has been just a f9w study reported on the design optimization for the acoustic radiation problems by using only the conventional BEM. For the thin-body acoustics, however, no further study in the optimization fields has been reported. In this research, the normal derivative integral equation is adopted as an analysis formulation in the thin-body acoustics, and then used fur the optimization. The analytical approaches for the design of holes are proposed by using a topology optimization technique and a genetic algorithm. The proposed approaches are implemented and validated using numerical examples.

• Structural Engineering and Mechanics
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• v.19 no.3
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• pp.281-295
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• 2005

An analytical method is presented to solve the elastodynamic problem of finitely long hollow cylinder subjected to torsional impact often occurs in engineering mechanics. The analytical solution is composed of a solution of quasi-static equation satisfied with the non-homogeneous boundary condition and a solution of dynamic equation satisfied with homogeneous boundary condition. The quasi-static solution is obtained directly by solving the quasi-static equation satisfied with the non-homogeneous boundary condition. The solution of the non-homogeneous dynamic equation is obtained by means of finite Hankel transform on the radial variable, r, Laplace transform on time variable, t, and finite Fourier transform on axial variable, z. Thus, the solution for finitely long, hollow cylinder subjected to torsion impact is obtained. In the calculating examples, the response histories and distributions of shear stress in the finitely long hollow cylinder subjected to an exponential decay torsion load are obtained, and the results have been analyzed and discussed. Finally, a dynamic finite element for the same problem is carried out by using ABAQUS finite element analysis. Comparing the analytical solution with the finite element solution, it can be found that two kinds of results obtained by means of two different methods agree well. Therefore, it is further concluded that the analytical method and computing process presented in the paper are effective and accurate.

• The Pure and Applied Mathematics
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• v.1 no.1
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• pp.29-33
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• 1994

There are various aspects of the solution of boundary-value problems for second-order linear elliptic equations in two independent variables. One useful method of solving such boundary-value problems for Laplace's equation is by means of suitable integral representations of solutions and these representations are obtained most directly in terms of particular singular solutions, termed Green's functions.(omitted)

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.70-77
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• 2002

Since our physical world cannot be modeled as rigid body, deformable object models are important. For real-time simulation of elastic object, it must be guaranteed by its exact solution and low-latency computational cost. In this paper, we describe the boundary integral equation formulation of linear elastic body and related boundary element method(BEM). The deformation of elastic body can be effectively solved with 1ow run-time computational costs, using precomputed Green Function and fast low-rank updates based on Capacitance Matrix Algorithm.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.46.1-46.1
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• 2019

We present an accurate and efficient method to calculate the gravitational potential of an isolated system in three-dimensional Cartesian and cylindrical coordinates subject to vacuum (open) boundary conditions. Our method consists of two parts: an interior solver and a boundary solver. The interior solver adopts an eigenfunction expansion method together with a tridiagonal matrix solver to solve the Poisson equation subject to the zero boundary condition. The boundary solver employs James's method to calculate the boundary potential due to the screening charges required to keep the zero boundary condition for the interior solver. A full computation of gravitational potential requires running the interior solver twice and the boundary solver once. We develop a method to compute the discrete Green's function in cylindrical coordinates, which is an integral part of the James algorithm to maintain second-order accuracy. We implement our method in the {\tt Athena++} magnetohydrodynamics code, and perform various tests to check that our solver is second-order accurate and exhibits good parallel performance.

• The Journal of the Acoustical Society of Korea
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• v.31 no.1
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• pp.19-28
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• 2012

The time-domain solution from the Kirchhoff integral equation for an exterior problem is not unique at certain eigen-frequencies associated with the fictitious internal modes as happening in frequency-domain analysis. One of the solution methods is the CHIEF (Combined Helmholtz Integral Equation Formulation) approach, which is based on employing additional zero-pressure constraints at some interior points inside the body. Although this method has been widely used in frequency-domain boundary element method due to its simplicity, it was not used in time-domain analysis. In this work, the CHIEF approach is formulated appropriately for time-domain acoustic boundary element method by constraining the unknown surface pressure distribution at the current time, which was obtained by setting the pressure at the interior point to be zero considering the shortest retarded time between boundary nodes and interior point. Sound radiation of a pulsating sphere was used as a test example. By applying the CHIEF method, the low-order fictitious modes could be damped down satisfactorily, thus solving the non-uniqueness problem. However, it was observed that the instability due to high-order fictitious modes, which were beyond the effective frequency, was increased.