• Computational Structural Engineering
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• v.11 no.4
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• pp.187-196
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• 1998

불연속 갤러킨 정식화에 기초를 둔 시간적분법에 대하여 시간을 변수로 한 유한요소적 접근법을 시도하였다. 단일 형상함수와 두 형상함수 정식화에 대해 각각 선형, 이차 형상함수를 적용하여 모두 네 종류의 시간적분법을 유도하였으며, 각 방법에 대하여 시간시텝의 증가에 따른 변위와 속도의 관계를 나타내는 증폭행렬을 계산하였다. 유도된 방법들의 성능을 평가하기 위하여 부하가 갑자기 변화는 진동 문제를 해석하고 변위의 오차를 비교하였다. 네 가지의 방법에 대하여 국부 오차 추정치를 개발하였으며, 오차 추정치의 정확도를 수치예를 이용하여 평가하였다. 단일 형상함수 정식화에서 이차 형상함수를 이용한 오차 추정치가 실제 국부오차를 잘 나타내었으며 유도된 오차 추정치는 시간간격제어 기법에서 시간간격의 크기를 결정하는 척도로 이용 가능하다.

• Computational Structural Engineering
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• v.6 no.4
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• pp.83-88
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• 1993

A time-discontinuous Galerkin method based upon using a finite element formulation in time has evolved. This method, working from the differential equation viewpoint, is different from those which have been generally used. They admit discontinuities with respect to the time variable at each time step. In particular, the elements can be chosen arbitrarily at each time step with no connection with the elements corresponding to the previous step. Interpolation functions and weighting functions are taken to be discontinuous across inter-element boundaries. These methods lead to a unconditional stable higher-order accurate ordinary differential equation solver.

• Journal of Advanced Navigation Technology
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• v.7 no.2
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• pp.180-190
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• 2003

By using accurate closed-form Green's functions obtained from real-axis integration method, the full-wave analysis of CPW discontinuities are performed in space domain. In solving MPIE(Mixed Potential Integral Equation), Galerkin's scheme is employed with the linear basis functions on the triangular elements in air-dielectric boundary. In the singular integral arising when the observation point and source point coincides, the surface integral is transformed into the line integral and the integral is evaluated by regular integration. By using the Green's function from the real-axis integration method, the discontinuities are characterized accurately.

• Journal of computational fluids engineering
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• v.19 no.3
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• pp.52-61
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• 2014

The present paper deals with the efficient computation of higher-order CFD methods for compressible flow using graphics processing units (GPU). The higher-order CFD methods, such as discontinuous Galerkin (DG) methods and correction procedure via reconstruction (CPR) methods, can realize arbitrary higher-order accuracy with compact stencil on unstructured mesh. However, they require much more computational costs compared to the widely used finite volume methods (FVM). Graphics processing unit, consisting of hundreds or thousands small cores, is apt to massive parallel computations of compressible flow based on the higher-order CFD methods and can reduce computational time greatly. Higher-order multi-dimensional limiting process (MLP) is applied for the robust control of numerical oscillations around shock discontinuity and implemented efficiently on GPU. The program is written and optimized in CUDA library offered from NVIDIA. The whole algorithms are implemented to guarantee accurate and efficient computations for parallel programming on shared-memory model of GPU. The extensive numerical experiments validates that the GPU successfully accelerates computing compressible flow using higher-order method.

• Nuclear Engineering and Technology
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• v.26 no.2
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• pp.212-224
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• 1994

A numerical method has been developed for studying the dynamics of a flexible cylinder in a coaxial cylindrical duct, immersed in inviscid flow. The unsteady inviscid fluid-dynamic force acting on the oscillating cylinder has been estimated more rigorously by means of a spectral collocation method without simplification of governing equations. This numerical approach is applicable to the system haying wider annular gap and/or shorter length of cylinder as compared to existing potential theory. The governing equation of the unsteady flow was obtained from Laplace equation. The equation of cylinder motion coupled with the fluid motion was discretized by Galerkin's method, from which the dynamic behaviour of the system has been evaluated. The effect of the length of the cylinder and the annular gap on the critical flour velocity, where the system loses stability by buckling, was investigated. To validate the numerical method, the potential flow theory developed by Hobson based on thin film approximation has been improved. Typical results of the present numerical theory on the dynamics and stability of the system are compared with those of available existing theory and the present approximate results. Good agreement was found between the results. It was also found that a nondimensional critical flow velocity becomes larger as increasing the annular gap and decreasing the length of cylinder.