• Title/Summary/Keyword: Absorbing boundary conditions

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Regularity of solutions to Helmholtz-type problems with absorbing boundary conditions in nonsmooth domains

  • Kim, Jinsoo;Dongwoo Sheen
    • Bulletin of the Korean Mathematical Society
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    • v.34 no.1
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    • pp.135-146
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    • 1997
  • For the numerical simulation of wave phenomena either in unbounded domains that it is not feasible to compute solutions on the entire region, it is needed to truncate the original domains to manageable bounded domains whose geometries are simple but usually nonsmooth. On the artificial boundaries thus created, absorbing boundary conditions are taken so that the significant part of waves arriving at the artificial boundaries can be transmitted [5,10,11,16,17,26]$.

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A Study on Improving The Capacity of Absorbing Boundary Using Dashpot (점성감쇠기를 이용하는 흡수경계의 성능 향상에 관한 연구)

  • Kim, Hee-Seok;Lee, Jong-Seh
    • Proceedings of the Earthquake Engineering Society of Korea Conference
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    • 2006.03a
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    • pp.440-444
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    • 2006
  • In this paper an analytical study is carried out to improve the capacity of absorbing boundary using dashpot, one of the most widely used absorbing boundaries in FEM. Using harmonic plane wave equation, absorbing boundary condition is modified to maximize its capacity according to the incident angle. Validity of the modified absorbing boundary conditions is investigated by adopting the solution of Miller-Pursey which is the solution for the wave propagation in semi-infinite elastic media, and the absorption ratio is calculated according to various Poisson's ratios.

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A Study on Finite Element Analysis with Paraxial Boundary Conditions for Elastic Wave Propagation (탄성파 진행 문제를 위한 Paraxial 경계조건의 유한요소해석에 관한 연구)

  • Kim, Hee-Seok;Lee, Jong-Seh
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2008.04a
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    • pp.33-38
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    • 2008
  • For the propagation of elastic waves in unbounded domains, absorbing boundary conditions at the fictitious numerical boundaries have been proposed. Paraxial boundary conditions(PBCs) which are kinds of absorbing boundary conditions based on paraxial approximations of the scalar and elastic wave equations not only lead to well-posed problem but also are stable and computationally inexpensive. But the complex mathematical forms of PBCs with partial derivatives complicate the application of those to finite element analysis. In this paper a penalty functional is newly proposed for applying PBCs into finite element analysis and the existence and uniqueness of the extremum of the proposed functional is demonstrated. The numerical verification of the efficiency is carried out through comparing PBCs with a viscous boundary condition.

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A Numerical Model of EM field calculation using Absorbing Boundary Conditions (Absorbing Boundary Condition을 이용한 전자파 수치해석)

  • Shin, Pan-Seok
    • Proceedings of the KIEE Conference
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    • 1990.11a
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    • pp.78-81
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    • 1990
  • The Engquist-Majdas second-order Absorbing Boundary Conditions (ABC) has been combined with the finite element formulation replacing the boundary integral equations in the hybrid finite-boundary element method (HEM). The method is applied to electromagnetic field radiation problems, especially to the microwave launcher, in order to verify the finite element formulation with the ABC's. The results with ABC are in good agreement with those of HEM. In order to see the applicability of the ABC, a simplified microwave oven utilizing ABC and an absorbing material are provided. The EM field distribution of the model is visualized. This method could be a useful analysis and design tool for EM field devices.

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Comparison of Absorbing Boundary Conditions and Waveguide Port Boundary Condition for Waveguide Electromagnetic Analysis Using Finite Element Method (유한요소법을 이용한 도파관 전자기 시뮬레이션에 있어 흡수경계조건 및 도파관 포트 경계조건 고찰 및 비교)

  • Mincheol Jo;Woobin Park;Woochan Lee
    • Journal of Internet Computing and Services
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    • v.24 no.2
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    • pp.27-36
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    • 2023
  • Waveguides are transmission lines that guide electromagnetic waves in the desired direction and are utilized in various fields such as medical devices, radar systems, and satellite communications. Computational electromagnetics (CEM) is essential for designing and optimizing waveguides. The finite element method (FEM), which is one of the numerical analysis techniques, is efficient in solving closed problems such as waveguides. In order to apply FEM for waveguide analysis, boundary conditions that truncate the computational domain are required. This paper performs electromagnetic simulations using absorbing boundary conditions (ABC) and waveguide port boundary conditions (WPBC) in 2/D and 3/D waveguides using the finite element method and compared their performances. The accuracy of the analysis was verified by comparing the results with HFSS, a representative commercial electromagnetic simulation software. Simulation results confirm that applying WPBC allows for smaller analysis domains than ABC.

A Study on the Performance of Absorbing Boundaries for Wave propagation Using Finite Element Method (유한요소법에서의 파진행 문제를 위한 흡수경계 성능에 관한 연구)

  • 김희석;이종세
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2003.10a
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    • pp.413-420
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    • 2003
  • In this paper an analytical study is carried out to examine the effectiveness of absorbing boundaries using dashpot. Validity of the absorbing boundary conditions suggested by Lysmer-Kuhlemeyer and White et al. is investigated by adopting the solution of Miller and Pursey. The Miller and Pursey's problem is then numerically simulated using the finite element method. The absorption ratios are calculated by comparing the displacements at the absorbing boundary to those at the free field without the absorbing boundary. The numerical verification is carried out through comparison of displacement at the boundary.

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A Study on Improving the Capacity of Absorbing Boundary Using Dashpot (점성감쇠기를 이용하는 흡수경계의 성능 향상에 관한 연구)

  • Kim, Hee-Seok;Lee, Jong-Seh
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.20 no.5
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    • pp.629-640
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    • 2007
  • In this paper an analytical study is carried out to improve the capacity of absorbing boundary using dashpot, one of the most widely used absorbing boundaries in FEM. Using 2-D harmonic plane wave equation, absorbing boundary condition is modified to maximize its capacity according to the incident angle. Validity of the absorbing boundary conditions which is modified is investigated by adopting the solution of Miller and Pursey. The Miller and Pursey's problem is then numerically simulated using the finite element method. The absorption ratios are calculated by comparing the displacements at the absorbing boundary to those at the free field without the absorbing boundary. The numerical study is carried out through comparison of displacement at the interior region and the boundary of the numerical model.

Finite Element Analysis with Paraxial Boundary Condition (파진행 문제를 위한 Paraxial 경계조건의 유한요소해석)

  • Kim, Hee-Seok;Lee, Jong-Seh
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2007.04a
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    • pp.475-480
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    • 2007
  • For the propagation of elastic waves in unbounded domains, absorbing boundary conditions at the fictitious numerical boundaries have been proposed. In this paper we focus on both first- and second-order paraxial boundary conditions(PBCs) in the framework of variational approximations which are based on paraxial approximations of the scalar and elastic wave equations- We propose a penalty function method for the treatment of PBCs and apply these into finite element analysis. The numerical verification of the efficiency is carried out through comparing PBCs with Lysmer-Kuhlemeyer' s boundary conditions.

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Comparisons between UPML and Liao's ABC in the FDTD method for 2D Cylindrical Coordinates (2D 원통형 좌표계를 위한 FDTD 방법에서 UPML과 Liao 흡수경계조건의 비교)

  • Hong, Ic-Pyo
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.11 no.6
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    • pp.1054-1061
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    • 2007
  • In this paper, the comparison between UPML and Liao's absorbing boundary condition in the FDTD(Finite-Difference Time-Domain) method was performed for the analysis of the 2D cylindrical coordinate system. Generally, it is known as the absorbing characteristics of the UPML is bro than Liao's absorbing boundary condition in the 2D rectangular coordinate. The simulation results in this paper showed that Liao's original absorbing boundary condition is better than other two absorbing boundary conditions, Liao's modified condition and UPML. We concluded that more numerical, theoretical studies, simulations and verifications for various absorbing boundary conditions will be needed to get more accurate results for the design of useful 2D cylindrical microwave circuits.

A Study on Absorbing Boundaries for Wave Propagation in Semi-Infinite Elastic Media (반무한 영역에서의 탄성파 진행문제를 위한 흡수경계에 관한 연구)

  • 이종세
    • Proceedings of the Earthquake Engineering Society of Korea Conference
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    • 2000.04a
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    • pp.451-457
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    • 2000
  • In many dynamic problems such as foundation vibrations ultrasonic nondestructive evaluation and blasting analysts are confronted with the problem of wave propagation in an infinite or semi-infinite media. In order to simulate this situation by a finite analytical model provisions must be made to absorb the stress waves arriving at the boundary. Absorbing boundaries are mathematical artifacts used to prevent wave reflections at the boundaries of discrete models for infinite media under dynamic loads. An analytical study is carried out to examine the effectiveness of Lysmer-Kuhlemeyer model one of the most widely used absorbing boundaries. Validity of the absorbing boundary conditions suggested by Lymer-Kuhlemeyer is examined by adopting the solution of Ewing et al. to the problem of plane waves from a harmonic normal force on the surface of an elastic half-space. The Ewing's problem is than numerically simulated using the finite element method on a semi-circular mesh with and without absorbing boundaries which are represented by viscous dashpots. The absorption ratios are calculated by comparing the displacements at the absorbing boundaries to those at the free field without absorbing boudaries.

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