• 한국항공운항학회지
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• 제16권2호
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• pp.21-27
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• 2008

An inverse method is introduced to construct the problem for the error analysis of the numerical solution of initial value problem. These problems constructed through this method have a known exact solution, even though analytical solutions are generally not obtainable. The process leading to the exact solution makes use of an initially available approximate numerical solution. A smooth interpolation of the approximate solution is forced to exactly satisfy the differential equation by analytically deriving a small forcing function to absorb all of the errors in the interpolated approximate solution. Using this special case exact solution, it is possible to investigate the relationship between global errors of a candidate numerical solution process and the associated tuning parameters for a given problem. Under the assumption that the original differential equation is well-posed with respect to the small perturbations, we thereby obtain valuable information about the optimal choice of the tuning parameters and the achievable accuracy of the numerical solution.

• Journal of Mechanical Science and Technology
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• 제17권4호
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• pp.538-544
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• 2003

Although many methodologies exist for determining the constrained equations of motion, most of these methods depend on numerical approaches such as the Lagrange multiplier's method expressed in differential/algebraic systems. In 1992, Udwadia and Kalaba proposed explicit equations of motion for constrained systems based on Gauss's principle and elementary linear algebra without any multipliers or complicated intermediate processes. The generalized inverse method was the first work to present explicit equations of motion for constrained systems. However, numerical integration results of the equation of motion gradually veer away from the constraint equations with time. Thus, an objective of this study is to provide a numerical integration scheme, which modifies the generalized inverse method to reduce the errors. The modified equations of motion for constrained systems include the position constraints of index 3 systems and their first derivatives with respect to time in addition to their second derivatives with respect to time. The effectiveness of the proposed method is illustrated by numerical examples.

• Journal of applied mathematics & informatics
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• 제39권5_6호
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1997년도 봄 학술발표회 논문집
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• pp.3-10
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• 1997

Meshless particle method is a numerical technique which does not use the concept of element. This method can easily handle special engineering problems which cause difficulty in the use of finite element method, however it has a drawback that essential boundary condition is not satisfied. In this paper, several studies for satisfying essential boundary conditions and enhancing the accuracy of solutions are discussed. Particular emphasis is placed on a new numerical technique in which finite elements are used on the boundaries to satisfy the essential boundary conditions and meshless particle method is used in the interior domain. For coupling of the two methods interface elements are introduced into the zone between the subdomains using meshless particle method and finite element method. The shape functions and the approximated displacement functions of the interface element are derived with the ramp function based on the shape function of finite elements. The whole numerical procedures are formulated by Galerkin method. Several numerical examples for enhancing the accuracy of solution in the meshless particle method and a new coupling method are presented.

• 한국항만학회지
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• 제10권1호
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• pp.53-61
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• 1996

This paper describes the effect of wave control using submerged flat plate by the numerical calculation and the hydraulic model test. The boundary element method is used to develop a numerical solution for the flow field caused by monochromatic oblique waves incident upon an infinitely long, sumerged flat plate situated in arbitrary water depth. The effect of wave blocking is examined according to the change of length, submerged depth of flat plate and incident angles. Numerical results show that longer length, shallower submergence of flat plate and larger incident angles enhance the effect of wave blocking. To validate numerical analysis method, hydraulic model test was conducted in 2-D wave flume with 60 cm metal sheet. Reflected waves are extracted from water surface elevation in front of the location of a submerged plate by least square method with 3 wave gages. From comparing experimental results with numerical results, efficiency of numerical analysis method by this study could be confirmed well within wide ranges of wave frequencies.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 봄 학술발표회 논문집
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• pp.76-83
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• 2001

In this study, a new method coupling of Element-Free Galerkin(EFG) method and Infinite Elements(IE) method is presented for extending application of the EFG method to engineering problems in unbounded domain. EFG method and IE method are briefly reviewed, and then the coupling procedure of the two methods is proposed. Numerical Algorithm by way of EFG-lE coupling technique is also developed. Numerical results illustrate the performance of the proposed technique. The accuracy of numerical solutions by the developed algorithm is guaranteed in comparing those of the other methods.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.657-670
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• 2015

In this paper, we provide numerical analysis of so-called Legendre Gauss-Radau and Legendre-Gauss collocation methods for ordinary differential equations. After recasting these collocation methods as Runge-Kutta methods, we prove that the Legendre-Gauss collocation method is equivalent to the well-known Gauss method, while the Legendre-Gauss-Radau collocation method does not belong to the classes of Radau IA or Radau IIA methods in the Runge-Kutta literature. Making use of the well-established theory of Runge-Kutta methods, we study stability and accuracy of the Legendre-Gauss-Radau collocation method. Numerical experiments are conducted to confirm our theoretical results on the accuracy and numerical stability of the Legendre-Gauss-Radau collocation method, and compare Legendre-Gauss collocation method with the Gauss method.

• 한국통신학회논문지
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• 제15권1호
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• pp.1-8
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• 1990

본 논문에서는 유전체 원통주의 전자파 과도 응답 산란 특성을 새로운 수치 해석 방법으로 연구하낟. 수치 해석에 사용하는 경계적분 방정식(BIE)의 기본 수식은 가중 잔차법으로 부터 시작된다. 경계 적분 방정식을 확장 경계 조건과 표면 경계 조건을 물체의 표면점 내부와 외부에 적용시켜 두개의 연립방정식을 만든다. 수치해석으로 경계요소법을 사용하고, 이 방법에는 직접법과 간접법 두 가지가 있다. 그래서 연산자를 메트릭스 역변환하는 간접법을 수치해석방법으로 사용한다. 결과값은 다른 연구 결과값과 좋은 일치를 보인다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 봄 학술발표회 논문집
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• pp.504-512
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• 2003

Simulation programs have been developed and used as an attempt to improve the accuracy of Non-Destructive Evaluation(NDE) techniques. The applicability of these programs is very limited, however, because it is difficult to describe the delicacy of the propagation of stress waves. To investigate the applicability of the finite element analysis for stress wave-based NDE techniques numerical simulation for Impact-Echo method and SASW method is performed. The numerical studies are performed to determine the essential parameters such as contact time of impact load, mesh size and time step size. These studies show that the choice of parameter is very important for improving the accuracy and confidence of the numerical procedure and, thereby, the applicability of the numerical analysis for stress wave-based NDE techniques

• 대한조선학회논문집
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• 제47권1호
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• pp.1-10
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• 2010

In the present paper, a numerical method based on the constraint interpolation profile (CIP) method is applied for simulating two-dimensional violent sloshing problems. The free surface boundary value problem is considered as a multiphase problem which includes water and air. A stationary Cartesian grid system is adopted, and an interface capturing method is used to trace the shape of free surface profile. The CIP combined unified procedure (CCUP) scheme is applied for flow solver, and the tangent of hyperbola for interface capturing (THINC) scheme is used for interface capturing. Numerical simulations have been carried out for partially-filled 2D tanks under forced sway and roll motions at various filling depths and frequencies. The computational results are compared with experiments and/or the other numerical results to validate the present numerical method.