• The Journal of the Korea Contents Association
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• v.11 no.1
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• pp.404-410
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• 2011

For the simulation of one-dimensional unsteady flow, the Taylor-Galerkin finite element method was adopted to the discretization of the Saint Venant equation. The model was applied to the backwater problem in a single channel and the flood routing in dendritic channel networks. The numerical solutions were compared with previously published results of finite difference and finite element methods and good agreement was observed. The model solves the continuity and the momentum equations in a sequential manner and this leads to easy implementation. Since the final system of matrix is tri-diagonal with a few additional entry due to channel junctions, the tri-diagonal matrix solution algorithm can be used with minor modification. So it is fast and economical in terms of memory for storing matrices.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.19 no.4
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• pp.108-116
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• 2005

This paper presents finite element analyses solution in the travelling magnetic field problem. The travelling magnetic field problem is subject to convective-diffusion equation. Therefore, the solution derived from Galerkin-FEM with linear interpolation function may oscillate between the adjacent nodes. A simple model with Dirichlet, Neumann and Periodic boundary condition respectively, have been analyzed to investigate stabilities of solutions. It is concluded that the solution of Galerkin-FEM may oscillate according to boundary condition and element type, but that of Upwind-FFM is stable regardless boundary condition.

• Journal of Korean Association for Spatial Structures
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• v.7 no.4
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• pp.55-61
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• 2007

Recently, with the development of computer, FEM has became the most frequently used numerical analysis method. FEM shows great ability in structures analysis, however, Galerkin's Method is more useful in grasping influence or the tendency of parameter which forms the structure. This paper perform the eigenvalue analysis using Galerkin's Method which is advantageous in grasping the influence and the tendency of parameter which forms the structure and study on the influence of parameter that forms arch on natural frequency response.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.2
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• pp.113-121
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• 2005

In order to resolve a common numerical integration inaccuracy of meshfree methods, we introduce an improved natural clement method called Petrov-Galerkin natural element method(PG-NEM). While Laplace basis function is being taken for the trial shape function, the test shape function in the present method is differently defined such that its support becomes a union of Delaunay triangles. This approach eliminates the inconsistency of tile support of integrand function with the regular integration domain, and which preserves both simplicity and accuracy in the numerical integration. In this paper, the validity of the PG-NEM is verified through the representative benchmark problems in 2-d linear elasticity. For the comparison, we also analyze the problems using the conventional Bubnov-Galerkin natural element method(BG-NEM) and constant strain finite clement method(CS-FEM). From the patch test and assessment on convergence rate, we can confirm the superiority of the proposed meshfree method.

• Proceedings of the KIEE Conference
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• 1997.07a
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• pp.174-176
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• 1997

편미분 방정식의 형태로 나타나는 많은 전자기장 문제들을 유한요소법이나 유한차분법 등의 수치해석적 방법으로 해결하려는 경우 시스템 행렬을 구성하게 된다. 이때 해석영역의 요소수가 많을수록 행렬의 조건수(condition number)는 다항식(polynomial) 증가를 갖게 되며, 이는 풀어야 할 선형시스템에서 반복 연산 과정의 속도를 떨어뜨리는 결과를 야기한다. 이러한 결과를 wavelet을 기저 함수로 쓰게 되면, 더 높은 분해능(resolution)의 해를 유한 요소법이나 유한 차분법에서와 같은 요소 분할 과정이 없이 Mallat 변환이라는 간단한 과정을 통해 구할 수 있으며, 본 논문에서는 Daubechies의 wavelet 함수를 기저 함수로 사용하여 전자기장 문제에 적용함으로서 수치해석에 있어서 wavelet 함수의 적용이 많은 장점을 갖고 있음을 보인다.

• Journal for History of Mathematics
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• v.18 no.4
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• pp.49-66
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• 2005

Finite element Methods(FEM) have been the primary computational methodologies in science and engineering computations for more than half centuries. One of the main limitations of the finite element approximations is that they need mesh which is an artificial constraint, and they need remeshing to solve in some special problems. The advantages in meshfree Methods is to develop meshfree interpolant schemes that only depends on particles, so they relieve the burden of remeshing and successive mesh generation. In this paper we describe the development of meshfree particle Methods and introduce the numerical schemes for Smoothed Particle hydrodynamics, meshfree Galerkin Methods and meshfree point collocation mehtods. We discusse the advantages and the shortcomings of these Methods, also we verify the applicability and efficiency of Meshfree Particle Methods.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.6 s.237
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• pp.703-710
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• 2005

A finite element discretization of the advection and redistancing equations of level set method has been studied. It has been shown that Galerkin spatial discretization combined with Crank-Nicolson temporal discretization of the advection equation of level set yields a good result and that consistent streamline upwind Petrov-Galerkin(CSUPG) discretization of the redistancing equation gives satisfactory solutions for two test problems while the solutions of streamline upwind Petrov-Galerkin(SUPG) discretization are dissipated by the numerical diffusion added for the stability of a hyperbolic system. Furthermore, it has been found that the solutions obtained by CSUPG method are comparable to those by second order ENO method.

• 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 Korea Water Resources Association
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• v.31 no.5
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• pp.599-612
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• 1998

Numerical analysis of convection-dominated transport problems are challenging because of dual characteristics of the governing equation. In the finite element method, a strategy is to modify the test function to weight more in the upwind direction. This is called as the Petrov-Galerkin method. In this paper, both N+1 and N+2 Petrov-Galerkin methods are applied to transport problems at high grid Peclet number. Frequency fitting algorithm is used to obtain optimal levels of N+2 upwinding, and the results are discussed. Also, a new Petrov-Galerkin method, named as "Optimal Test Function Petrov-Galerkin Method," is proposed in this paper. The test function of this numerical method changes its shape depending upon relative strength of the convection to the diffusion. A numerical experiment is carried out to demonstrate the performance of the proposed method.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.14 no.4
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• pp.321-328
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• 1989

The propagation characteristics of dielectric waveguides has been analyzed by finite element method. We have proposed the finite element formutation of the variational expression in the three-component magnetic field based on Galerkin's method which seek for the propagation constant by a given value of frequency. In this approach, the divergence relation for H is satisfied and spurious modes does not appear and finite element solustions agree with the exact solutions. In order to varify the validity of the present method the numerical results for a rectangular waveguide partilly filled with dielectric are compared with other results.