• Proceedings of the Computational Structural Engineering Institute Conference
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• 한국전산구조공학회 1994년도 봄 학술발표회 논문집
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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 applied mathematics & informatics
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• 제26권5_6호
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• pp.1273-1287
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• 2008

In this paper, the numerical integration method for general singularly perturbed two point boundary value problems with mixed boundary conditions of both left and right end boundary layer is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.557-581
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• 2022

The anisotropic-diffusion convection equation with exponentially variable coefficients is discussed in this paper. Numerical solutions are found using a combined Laplace transform and boundary element method. The variable coefficients equation is usually used to model problems of functionally graded media. First the variable coefficients equation is transformed to a constant coefficients equation. The constant coefficients equation is then Laplace-transformed so that the time variable vanishes. The Laplace-transformed equation is consequently written as a boundary integral equation which involves a time-free fundamental solution. The boundary integral equation is therefore employed to find numerical solutions using a standard boundary element method. Finally the results obtained are inversely transformed numerically using the Stehfest formula to get solutions in the time variable. The combined Laplace transform and boundary element method are easy to implement and accurate for solving unsteady problems of anisotropic exponentially graded media governed by the diffusion convection equation.

• Journal of applied mathematics & informatics
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• 제8권1호
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• pp.129-136
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• 2001

We introduce and discuss a new numerical method for solving system of second order boundary value problems, where the solution is required to satisfy some extra continuity conditions on the subintervals in addition to the usual boundary conditions. We show that the present method gives approximations which are better than that produced by other collocation, finite difference and spline methods. Numerical example is presented to illustrate the applicability of the new method. AMS Mathematics Subject Classification : 65L12, 49J40.

• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.13-22
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• 2019

This paper presents a symbolic method for solving a boundary value problem with inhomogeneous Stieltjes boundary conditions over integro-differential algebras. The proposed symbolic method includes computing the Green's operator as well as the Green's function of the given problem. Examples are presented to illustrate the proposed symbolic method.

• International Journal of Aeronautical and Space Sciences
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• 제13권1호
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• pp.43-57
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• 2012

In a modern aircraft, there are many variations in its mass, stiffness, and aerodynamic characteristics. Recently, an analytical approach was proposed, and this approach uses the idea of uncertainty to find out the most critical flight flutter boundary due to the variations in such aerodynamic characteristics. An analytical method that has been suggested to predict robust stability is the mu method. We previously analyzed the robust flutter boundary by using the mu method, and in that study, aerodynamic variations in the Mach number, atmospheric density, and flight speed were taken into consideration. The authors' previous attempt and the results are currently quoted as varying Mach number mu analysis. In the author's previous method, when the initial flight conditions were located far from the nominal flutter boundary, conservative predictions were obtained. However, relationships among those aerodynamic parameters were not applied. Thus, the varying Mach number mu analysis results required validation. Using an optimization approach, the varying Mach number mu analysis was found out to be capable of capturing a reasonable robust flutter boundary, i.e., with a low percentage difference from boundaries that were obtained by optimization. Regarding the optimization approach, a discrete nominal flutter boundary is to be obtained in advance, and based on that boundary, an interpolated function was established. Thus, the optimization approach required more computational effort for a larger number of uncertainty variables. And, this produced results similar to those from the mu method which had lower computational complexity. Thus, during the estimation of robust aeroelastic stability, the mu method was regarded as more efficient than the optimization method was. The mu method predicts reasonable results when an initial condition is located near the nominal flutter boundary, but it does not consider the relationships that are among the aerodynamic parameters, and its predictions are not very accurate when the initial condition is located far from the nominal flutter boundary. In order to provide predictions that are more accurate, the relationships among the uncertainties should also be included in the mu method.

• The Bulletin of The Korean Astronomical Society
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• 제44권2호
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• pp.69.2-69.2
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• 2019

To construct a coronal force-free magnetic field, we must impose the boundary normal current density (or three components of magnetic field) as well as the boundary normal field at the photosphere as boundary conditions. The only method that is known to implement these boundary conditions exactly is the method devised by Grad and Rubin (1958). However, the Grad-Rubin method and all its variations (including the fluxon method) suffer from convergence problems. The magnetofrictional method and its variations are more robust than the Grad-Rubin method in that they at least produce a certain solution irrespective of whether the global solution is compatible with the imposed boundary conditions. More than often, the influence of the boundary conditions does not reach beyond one or two grid planes next to the boundary. We have found that the 2D solenoidal gauge condition for vector potentials allows us to implement the required boundary conditions easily and effectively. The 2D solenoidal condition is translated into one scalar function. Thus, we need two scalar functions to describe the magnetic field. This description is quite similar to the Chandrasekhar-Kendall representation, but there is a significant difference between them. In the latter, the toroidal field has both Laplacian and divergence terms while in ours, it has only a 2D Laplacian term. The toroidal current density is also expressed by a 2D Laplacian. Thus, the implementation of boundary normal field and current are straightforward and their effect can permeate through the whole computational domain. In this paper, we will give detailed math involved in this formulation and discuss possible lateral and top boundary conditions and their meanings.

• Korea-Australia Rheology Journal
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• 제13권1호
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• pp.37-45
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• 2001

Numerical simulation of coextrusion process of viscoelastic fluids within a die has been carried out. In the coextrusion process velocity profile at the outflow boundary is not known a priori, which makes it difficult to impose the proper boundary condition at the outflow boundary. This difficulty has been avoided by using the open boundary condition (OBC) method. In this study, elastic viscous stress splitting (EVSS) formulation with streamline upwind (SU) method has been used in the finite element method. In order to test the validity of the OBC method, comparison between the results of fully developed condition at the outlet and those of OBC has been made for a Newtonian fluid. In the case of upper convected Maxwell (UCM) fluid, the effect of outflow boundary condition on the interface position has been investigated by using two meshes having different downstream lengths. In both cases, the results with the OBC method showed reasonable interface shape. In particular, for the UCM fluid the interface shape calculated with OBC was independent of the downstream length, while the results with the zero traction condition showed oscillation of interface position close to the outlet. Viscosity difference was found to be more important than elasticity difference in determining the final interface position. However, the overshoot of interface position near the con-fluent point increased with elasticity.

• Journal of the Society of Naval Architects of Korea
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• 제39권4호
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• pp.1-10
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• 2002

For the time-domain simulation of incipient breaking waves, usually the boundary integral method has been used so far, and it seems to be successful except a problem of too much computation time. The present paper shows a new computation technique for the simulation of breaking wave experiment. This technique uses the high-order spectral/boundary element method and the boundary integral method in sequence, and reduces the computation time remarkably. The wave generation and energy focusing process is efficiently simulated by the high-order spectral/boundary element method. Only the wave over-turning process is simulated by the boundary integral method. In the example calculation result, salient features of breaking waves such as high particle velocities and accelerations are shown.

• Journal of the Korean Geosynthetics Society
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• 제20권3호
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• pp.11-20
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• 2021

In this paper, the approximately coupled method of finite element method and boundary element method to obtain efficient and accurate analysis results is proposed for a two-dimensional elasto-static problem with a geometrically abruptly changing part. As the finite element of a two-dimensional problem, three-node and four-node plane stress element is applied, and as the boundary element of a two-dimensional problem, three-node boundary element is applied. In the modeling stage, firstly, an entire analysis target object is modeled as finite elements, and then a geometrically abruptly changing part is modeled as boundary elements. The boundary element is defined using the nodes defined for modeling finite elements. In the analysis stage, finite element analysis is firstly performed on a entire analysis target object, and boundary element analysis is automatically performed afterwards. As for the boundary conditions at boundary element analysis, displacement conditions and stress conditions, which are the results of finite element analysis, are applied. As a numerical example, the analysis results for a two-dimensional elasto-static problem, a plate with a crack, are presented and investigated.