• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.2
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• pp.113-120
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• 2021

The wave-propagation phenomenon in an infinite medium has been used to describe the physics in many fields of engineering and natural science. Analytical or numerical methods have been developed to obtain solutions to problems related to the wave-propagation phenomenon. Energy radiation into infinite regions must be accurately considered for accurate solutions to these problems; hence, various numerical and mechanical models as well as boundary conditions have been developed. This paper proposes a new boundary condition that can be applied to scalar-wave or horizontally-polarized shear-wave (or SH-wave) propagation problems in layered waveguides. A governing equation is obtained for the SH waves by applying finite-element discretization in the vertical direction of the waveguide and subsequently modified to derive the boundary condition for the infinite region of the waveguide. Using the orthogonality of the eigenmodes for the SH waves in a layered waveguide, the new boundary condition is shown to be equivalent to the existing root-finding absorbing boundary condition; further, the accuracy is shown to increase with the degree of the new boundary condition, and its stability can be proven. The accuracy and stability are then demonstrated by applying the proposed boundary condition to wave-propagation problems in layered waveguides.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1991.04a
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• pp.8-14
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• 1991

The finite element technique incorporating infinite elements is applied to analyzing the general three dimensional wave-structure interaction problems within the limits of linear wave theory. The hydrodynamic farces are assumed to be inertially dominated, and viscous effects are neglected. In order to analyze the corresponding boundary value problems efficiently, two types of elements are developed. One is the infinite element for modeling the radiation condition at infinity, and the other is the fictitious bottom boundary element for the case of deep water. To validate those elements, numerical analyses are performed for several floating structures. Comparisons with the results from culler available solution methods show that the present method incorporating tile infinite and the fictitious bottom boundary elements gives good results.

• Journal of the Korean Geosynthetics Society
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• v.6 no.3
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• pp.9-16
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• 2007

Soil vapor extraction (SVE) is an effective and cost efficient method of removing volatile organic compounds (VOCs) and petroleum hydrocarbons from unsaturated soils. Incorporating PVDs in an SVE system can extend the effectiveness of SVE to lower permeability soils by shortening the air flow-paths and ultimately expediting contaminant removal. With this approach, the real bounded system is replaced for the purposes of analysis by an imaginary system of infinite areal extent. The boundary conditions for the contaminant remediation model test include constant head and no flow condition. Due to these parallel boundaries conditions, image wells should be developed in order to maintain the condition of no flow across the impermeable boundary. It is also assumed that the flow is drawdown along the constant head boundary condition. The factors contributing to the difference between the theoretical and measured pressure heads were also analyzed. The flow factor increases as the flow rate is increased. The flow rate is the most important factor that affects the difference between the measured and theoretical pressure heads.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1994.04a
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• pp.128-136
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• 1994

In this study, dynamic boundary element method using mass matrix is derived, using fundamental solutions for the semi-infinite domain. In constituting boundary integral equations for the dynamic equilibrium condition, inertia term in the form of domain integral is transformed into boundary integral form. Corresponding system equations are derived, and a boundary element program is developed. In addition, equations for free vibration is formulated, and eigenvalue analysis is performed. The results from the dynamic boundary element analysis for a tunnel problem are compared with those from the finite element analysis. According to the comparison, boundary element method using mass matrix is consistent with the results of finite element method. Consequently, in tunnel vibration problems, it results in reasonable solution compared with other methods where relatively higher degree of freedoms are employed.

• Journal of the Optical Society of Korea
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• v.9 no.2
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• pp.39-44
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• 2005

Unlike for the bound states, several different boundary conditions are used for the continuum states above the barrier in semiconductor quantum wells. We employed three boundary conditions, infinite potential barrier boundary condition, periodic boundary condition and scattering boundary condition, and calculated the local number of states, wavefunctions and optical matrix elements for the symmetric and asymmetric quantum wells. We discussed how these quantities are related in the three boundary conditions. We argue that the scattering boundary condition has several advantages over the other two cases. These results would be useful in understanding quantum well lasers and detectors involving continuum states.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2002.09a
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• pp.280-282
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• 2002

In analysis of pumping test data, generally infinite domain has been assumed. However, in many cases, this assumption was not readily satisfied. Some boundaries conditions and natural heterogeneity of hydrogeologic properties would play critical roles on groundwater flow and contaminant transport. This study examined effects of some boundary conditions and heterogeneity on the groundwater flow and contaminant transport with basic numerical groundwater modeling, which provides implications for remediation of contaminated groundwater.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.1
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• pp.39-61
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• 2017

In this present article, we analyzed the heat and mass transfer characteristics of the nonlinear unsteady radiative MHD flow of a viscous, incompressible and electrically conducting fluid past an infinite vertical porous plate under the influence of Soret and chemical reaction effects. The effect of physical parameters are accounted for two distinct types of thermal boundary conditions namely prescribed uniform wall temperature thermal boundary condition and prescribed heat flux thermal boundary condition. Based on the flow nature, the dimensionless flow governing equations are resolved to harmonic and non harmonic parts. In particular skin friction coefficient, Nusselt number and Sherwood number are found to evolve into their steady state case in the large time limit. Parametric study of the solutions are conducted and discussed.

• Geophysics and Geophysical Exploration
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• v.11 no.2
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• pp.153-160
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• 2008

Seismic modeling is used to simulate wave propagation in the earth. Although the earth's subsurface is usually semi-infinite, we cannot handle the semi-infinite model in seismic modeling because of limited computational resources. For this reason, we usually assume a finite-sized model in seismic modeling. In that case, we need to eliminate the edge reflections arising from the artificial boundaries introducing a proper boundary condition. In this study, we changed three kinds of boundary conditions (sponge boundary condition, Clayton and Engquist's absorbing boundary condition, and Higdon's transparent boundary condition) so that they can be applied in elastic wave modeling for anisotropic media. We then apply them to several models whose Poisson's ratios are different. Clayton and Engquist's absorbing boundary condition is unstable in both isotropic and anisotropic media, when Poisson's ratio is large. This indicates that the absorbing boundary condition can be applied in anisotropic media restrictively. Although the sponge boundary condition yields good results for both isotropic and anisotropic media, it requires too much computational memory and time. On the other hand, Higdon's transparent boundary condition is not only inexpensive, but also reduce reflections over a wide range of incident angles. We think that Higdon's transparent boundary condition can be a method of choice for anisotropic media, where Poisson's ratio is large.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1998.04a
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• pp.98-105
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• 1998

In this study, the boundary element analysis in dynamics for the multilayered semi-infinite plane is developed using the fundamental solution for moving loads. Also the indirect method and superposition method are introduced to consider the multilayered systems and moving loads. At each layer the fundamental solution can be obtained by solving the governing equation which is transformed by the Fourier transform. The governing equation can be solved by three conditions; continuity conditions of displacement and stress, the traction free condition at the surface and the radiation condition at the surface and the radiation condition at the infinite distance. To verify the solution and the developed algorithm, the theoretical solution for the homogeneous layer and commercial FEM program is compared with the results of this study.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.6 no.2
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• pp.139-149
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• 1994

In this paper, a finite element technique is applied to the prediction of the wave resonance phenomena in harbors. The mild-slope equation is used with a partial reflection boundary condition introduced to model the energy dissipating effects on the solid boundary. For an efficient modeling of the radiation condition at infinity, a new infinite element is developed. The shape function of the infinite element is derived from the asymptotic behavior of the first kind of the Hankel's function in the analytical boundary series solutions. For the computational efficiency, the system matrices of the element are constructed by performing the relevant integrations in the infinite direction analytically. Comparisons with the results from experiments and other solution methods show that the present model gives fairly good results. Numerical experiments are also carried out to determine the proper distance to the infinite elements from the mouth of the halter, which directly affect the accuracy and efficiency of the solution.