• Title, Summary, Keyword: free boundary

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Free Vibration Analysis of Arbitrarily Shaped Plates with Free Edges using Non-dimensional Dynamic Influence Functions (무차원 동영향 함수를 이용한 자유단 경계를 가진 임의 형상 평판의 자유진동해석)

  • Gang, S.W.;Kim, I.S.;Lee, J.M.
    • Proceedings of the KSME Conference
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    • pp.740-745
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    • 2003
  • The so-called boundary node method (or NDIF method) that was developed by the authors has been extended for free vibration analysis of arbitrarily shaped plates with free edges. Since the proposed method is based on the collocation method, no integration procedure is needed on boundary edges of the plates and only a small amount of numerical calculation is required. A special coordinate transformation has been devised to consider the complicated free boundary conditions at boundary nodes. By the use of the special coordinate transformation, the radius of curvature involved in the free boundary conditions can be successfully dealt with. Finally, verification examples show that natural frequencies obtained by the present method agree well with those given by exact method and other analytical methods.

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A hopf bifurcation on a parabolic free boundary problem with pushchino dynamics

  • Ham, Yoon-Mee;Seung, Byong-In
    • Journal of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.237-250
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    • 1995
  • A hopf bifurcation of a free boundary (or an internal layer) occurs in solidification, chemical reactions and combustion. It is a well-known fact that a free boundary usually appear as sharp transitions with narrow width between two materials ([2]).

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A coupled Ritz-finite element method for free vibration of rectangular thin and thick plates with general boundary conditions

  • Eftekhari, Seyyed A.
    • Steel and Composite Structures
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    • v.28 no.6
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    • pp.655-670
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    • 2018
  • A coupled method, that combines the Ritz method and the finite element (FE) method, is proposed to solve the vibration problem of rectangular thin and thick plates with general boundary conditions. The eigenvalue partial differential equation(s) of the plate is (are) first reduced to a set of eigenvalue ordinary differential equations by the application of the Ritz method. The resulting eigenvalue differential equations are then reduced to an eigenvalue algebraic equation system using the finite element method. The natural boundary conditions of the plate problem including the free edge and free corner boundary conditions are also implemented in a simple and accurate manner. Various boundary conditions including simply supported, clamped and free boundary conditions are considered. Comparisons with existing numerical and analytical solutions show that the proposed mixed method can produce highly accurate results for the problems considered using a small number of Ritz terms and finite elements. The proposed mixed Ritz-FE formulation is also compared with the mixed FE-Ritz formulation which has been recently proposed by the present author and his co-author. It is found that the proposed mixed Ritz-FE formulation is more efficient than the mixed FE-Ritz formulation for free vibration analysis of rectangular plates with Levy-type boundary conditions.

THE NON-EXISTENCE OF HOPE BIFURCATION IN A DOUBLE-LAYERED BOUNDARY PROBLEM SATISFYING THE DIRICHLET BOUNDARY CONDITION

  • Ham, Yoon-Mee
    • Communications of the Korean Mathematical Society
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    • v.14 no.2
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    • pp.441-447
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    • 1999
  • A free boundary problem is derived from a singular limit system of a reaction diffusion equation whose reaction terms are bistable type. In this paper, we shall consider a free boundary problem with two layers satisfying the zero flux boundary condition and shall show that the Hopf bifurcation can not occur as a parameter varies.

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A Study on the Treatment of Open Boundary in the Two-Dimensional Free-Surface Wave Problems

  • Kim, Yong-Hwan
    • Selected Papers of The Society of Naval Architects of Korea
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    • v.2 no.1
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    • pp.63-78
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    • 1994
  • This paper deals with the treatment of the open boundary in two-dimensional free-surface wave problems. Two numerical schemes are investigated for the implementation of the open boundary condition. One is to add the artificial damping term to the dynamic free-surface boundary condition, in which the determination of suitable damping coefficient and the damping zone is the most important. The other is a modified Orlanski's method, which is known to be very useful for the uni-directional waves. Using these two schemes, numerical tests have been conducted for a few typical free-surface wave problems. To obtain the numerical solution of the free-surface boundary value problem, the fundamental source-distribution method is used and the fully nonlinear free-surface boundary conditions are applied. The computed results are presented in comparison with those of others for the proof of practicality of these two schemes.

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Cause Analysis and Removal of Boundary Artifacts in Image Deconvolution

  • Lee, Ji-Yeon;Lee, Nam-Yong
    • Journal of Korea Multimedia Society
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    • v.17 no.7
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    • pp.838-848
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    • 2014
  • In this paper, we conducted a cause analysis on boundary artifacts in image deconvolution. Results of the cause analysis show that boundary artifacts are caused not only by a misuse of boundary conditions but also by no use of the normalized backprojection. Results also showed that the correct use of boundary conditions does not necessarily remove boundary artifacts. Based on these observations, we suggest not to use any specific boundary conditions and to use the normalized backprojector for boundary artifact-free image deconvolution.

FINITE ELEMENT METHODS FOR THE PRICE AND THE FREE BOUNDARY OF AMERICAN CALL AND PUT OPTIONS

  • Kang, Sun-Bu;Kim, Taek-Keun;Kwon, Yong-Hoon
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.12 no.4
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    • pp.271-287
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    • 2008
  • This paper deals with American call and put options. Determining the fair price and the free boundary of an American option is a very difficult problem since they depends on each other. This paper presents numerical algorithms of finite element method based on the three-level scheme to compute both the price and the free boundary. One algorithm is designed for American call options and the other one for American put options. These algorithms are formulated on the system of the Jamshidian equation for the option price and the free boundary. Here, the Jamshidian equation is of a kind of the nonhomogeneous Black-Scholes equations. We prove the existence and uniqueness of the numerical solution by the Lax-Milgram lemma and carried out extensive numerical experiments to compare with various methods.

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