• 한국지구물리탐사학회:학술대회논문집
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• 한국지구물리탐사학회 2008년도 공동학술대회
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• pp.57-62
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• 2008

탄성파 수치 모형 계산에 있어서 널리 사용되는 엇갈린 격자 방법이 아니라 회전된 엇갈린 격자 방법을 사용하여 탄성파 수치 모사를 수행하였다. 표준 엇갈린 격자 방법에서는 자유 경계조건을 적용하여야 하는 단점이 있지만 회전된 격자 방법에서는 자유 경계조건을 적용할 필요 없이 물성을 부여함으로써 해결될 수 있다. 파동전파에 있어서 유한 경계 조건에서 발생하는 인공 반사파를 제거하기 위하여 최근에 뛰어난 성능을 보이는 PML(Perfectly Matched Layer)법이 많이 적용되고 있다. 이 연구에서는 PML보다 성능이 뛰어나기도 하지만 차분에 있어 파동식을 분리할 필요가 없는 CPML(Convolutional Perfectly Matched Layer)법을 회전된 엇갈린 격자법(RSG : Rotatged Staggered Grid)에 적용하고자 하였다. Cerjan법의 감쇠법과 비교한 결과 매우 효과적으로 인공 반사파를 제거할 수 있음을 알 수 있었다.

• Earthquakes and Structures
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• 제3권3_4호
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• pp.383-411
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• 2012

The objective of the present paper is to review and implement the most recent developments in the Spectral Element Method (SEM), as well as improve aspects of its implementation in the study of wave propagation by numerical simulation in elastic unbounded domains. The classical formulation of the method is reviewed, and the construction of the mass matrix, stiffness matrix and the external force vector is expressed in terms of matrix operations that are familiar to earthquake engineers. To account for the radiation condition at the external boundaries of the domain, a new absorbing boundary condition, based on the Perfectly Matched Layer (PML) is proposed and implemented. The new formulation, referred to as the Multi-Axial Perfectly Matched Layer (M-PML), results from generalizing the classical Perfectly Matched Layer to a medium in which damping profiles are specified in more than one direction.

• 지구물리와물리탐사
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• 제12권2호
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• pp.183-191
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• 2009

탄성파 수치 모형 계산에 있어서 널리 사용되는 엇갈린 격자 방법이 아니라 회전된 엇갈린 격자 방법을 사용하여 탄성파 수치 모사를 수행하였다. 표준 엇갈린 격자 방법에서는 특별한 자유 경계조건을 적용하여야 하는 단점이 있지만 회전된 격자 방법에서는 물성으로 진공 또는 공기층을 부여함으로써 자유 경계조건을 실현가능하다는 것을 확인할 수 있었다. 파동전파에 있어서 유한 경계 조건에서 발생하는 인공 반사파를 제거하기 위해 PML (Perfectly Matched Layer)의 파동식 분해라는 단점을 극복할 수 있고 좋은 성능을 보이는 CPML (Convolutional Perfectly Matched Layer)법을 회전된 엇갈린 격자법(RSG: Rotatged Staggered Grid)에 적용하였다. 회전된 격자 유한 차분법에서 CPML의 고주파수 흡수 특성과 에너지 흡수율 조사, Cerjan법의 감쇠를 비교한 결과 흡수경계조건으로 좋은 성능을 확인하였다. 유체와 고체의 모형에 대한 경계에 대하여서도 매우 효과적으로 경계면에서 발생하는 반사파를 제거할 수 있음을 알 수 있었다.

• 한국전자파학회논문지
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• 제11권4호
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• pp.592-598
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• 2000

The existin Berenger's PML(Perfectly Matched Layer) cannot absorb evanescent modes effectively generated in waveguides or periodic array structures. Although some absorbing boundary conditons(ABC) were introduced to absorp the evanescent modes, they did not show sufficient performance or could not be applied easily because of their much difference from Berengers PML. In this paper, NPML(New PML) is introduced to absorb the evanescent modes by splitting the conductivity and permittivity profile of the Berengers PML. The proposed NPML is certified as an ABC having enough performance for evanescent and propagating modes by analyzing the global error and the reflectivity of a waveguide.

• Earthquakes and Structures
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• 제3권3_4호
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• pp.563-580
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• 2012

We modify the formulation of a recently developed absorbing boundary condition (ABC), the perfectly matched discrete layers (PMDL), to incorporate the excitation coming from the exterior such as earthquake waves. The modified formulation indicates that the effect of the exterior excitation can be incorporated into PMDL ABCs (traditionally designed to treat only interior excitation) simply by applying appropriate forces on the nodes connected to the first PMDL layer. Numerical results are presented to clearly illustrate the effectiveness of the proposed method.

• The Journal of the Acoustical Society of Korea
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• 제25권3E호
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• pp.131-136
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• 2006

The PML developed for the radio wave propagation is a powerful numerical domain truncation technique. We perform an analytic study on the reflection from the PML inserted in the ocean bottom. In the ocean bottom, we show the PML to have the improved performance but simultaneously the degeneration below the critical angle of the fast ocean bottom. The degeneration of the PML can be simply relaxed by stretching the thickness of the PML or putting the attenuation coefficient to the ocean bottom. As a better solution, we propose the improved truncation technique based on the PML and the non-local boundary condition. Finally, we apply the PML to the acoustic wave propagation using split-step Pade PE solver. For the problems of the ocean waveguide, the numerical efficiency of the PML is examined and the usefulness of the PML is confirmed.

• 지구물리와물리탐사
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• 제15권2호
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• pp.57-65
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• 2012

탄성파 수치 모형 계산에 있어서 다양한 방법들이 개발되어 적용되었다. 최근에는 특히 탄성파 수치 모형 계산에 있어 혁신적인 방법인 SEM (Spectral Element Method)가 개발되어 사용되어 왔다. 이 방법은 지형을 자유롭게 표현하는데 있어 유연한 유한요소법의 장점에 정확성을 높인 방법이다. 일반적으로 Weak Formulation 형태의 파동방정식에 육면체 요소와 Gauss-Lobatto-Legendre 적분법을 적용한 방법이 널리 사용된다. 일반적인 SEM에서는 PML (Perfectly Matched Layer)경계조건을 적용하기 어려워 속도-응력 변분식으로 파동방정식을 변경하였다. CFS-PML (Complex frequency Shifted PML)경계조건을 ADE (Auxiliary Differential Equation)방정식으로 변경하여 속도-응력 파동방정식에 적용함으로써 분리할 필요가 없는 PML을 적용한 SEM 수치 모형 계산 알고리듬을 구현하였다. 1차원 수치모형과 3차원 수치모형 실험을 통하여 SEM에 적용한 비분리 CFS-PML이 유한경계에서 인공적으로 반사되는 반사파를 효과적으로 제거하는 것을 확인하였다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2012년도 춘계학술대회 논문집
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• pp.521-526
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• 2012

It is essential for the accurate time-domain prediction of broadband noise due to turbulence-cascade interaction to develop inflow/outflow boundary conditions to satisfy the following three requirements: to maintain the back ground mean flow, to nonreflect the outgoing disturbances and to generate the specified input gust. The preceding study(1) showed that Perfectly Matched Layer (PML) boundary condition was successfully applied to absorb the outgoing disturbances and to generate the specified gust in the time-domain computations of broadband noise due to interaction of incident gust with a cascade of flat-plates. In present study, PML boundary condition is extended in order to predict steady mean flow that is needed for the computation of noise due to interaction of incident gust with a cascade of airfoils. PML boundary condition is originally designed to absorb flow disturbances superimposed on the steady meanflow in the buffer zone. However, the steady meanflow must be computed before PML boundary condition is applied on the flow computation. In the present paper, PML equations are extended by introducing source term to maintain desired mean flow conditions. The extended boundary condition is applied to the benchmark problem where the meanflow around a cascade of airfoils is predicted. These illustrative computations reveal that the extended PML equations can effectively provide and maintain the target meanflow.

• 한국소음진동공학회논문집
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• 제22권7호
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• pp.685-691
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• 2012

It is essential for the accurate time-domain prediction of broadband noise due to turbulence-cascade interaction to develop inflow/outflow boundary conditions to satisfy the following three requirements: to maintain the back ground mean flow, to nonreflect the outgoing disturbances and to generate the specified input gust. The preceding study showed that perfectly matched layer(PML) boundary condition was successfully applied to absorb the outgoing disturbances and to generate the specified gust in the time-domain computations of broadband noise due to interaction of incident gust with a cascade of flat-plates. In present study, PML boundary condition is extended in order to predict steady mean flow that is needed for the computation of noise due to interaction of incident gust with a cascade of airfoils. PML boundary condition is originally designed to absorb flow disturbances superimposed on the steady meanflow in the buffer zone. However, the steady meanflow must be computed before PML boundary condition is applied on the flow computation. In the present paper, PML equations are extended by introducing source term to maintain desired mean flow conditions. The extended boundary condition is applied to the benchmark problem where the meanflow around a cascade of airfoils is predicted. These illustrative computations reveal that the extended PML equations can effectively provide and maintain the target meanflow.

• Structural Engineering and Mechanics
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• 제51권4호
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• pp.685-705
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• 2014

This paper presents a new formulation for forward scalar wave simulations in semi-infinite media. Perfectly-Matched-Layers (PMLs) are used as a wave absorbing boundary layer to surround a finite computational domain truncated from the semi-infinite domain. In this work, a hybrid formulation was developed for the simulation of scalar wave motion in two-dimensional PML-truncated domains. In this formulation, displacements and stresses are considered as unknowns in the PML domain, while only displacements are considered to be unknowns in the interior domain. This formulation reduces computational cost compared to fully-mixed formulations. To obtain governing wave equations in the PML region, complex coordinate stretching transformation was introduced to equilibrium, constitutive, and compatibility equations in the frequency domain. Then, equations were converted back to the time-domain using the inverse Fourier transform. The resulting equations are mixed (contain both displacements and stresses), and are coupled with the displacement-only equation in the regular domain. The Newmark method was used for the time integration of the semi-discrete equations.