• 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 Computational Structural Engineering Institute of Korea
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• v.18 no.2
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• pp.123-131
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• 2005

According to ow previous study, we confirmed That the Petrov-Galerkin natural element method(PG-NEM) completely resolves the numerical integration inaccuracy in the conventional Bubnov-Galerkin natural element method(BG-NEM). This paper is an extension of PG-NEM to two-dimensional geometrically nonlinear problem. For the analysis, a linearized total Lagrangian formulation is approximated with the PS-NEM. At every load step, the grid points ate updated and the shape functions are reproduced from the relocated nodal distribution. This process enables the PG-NEM to provide more accurate and robust approximations. The representative numerical experiments performed by the test Fortran program, and the numerical results confirmed that the PG-NEM effectively and accurately approximates The large deformation problem.

• Computers and Concrete
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• v.23 no.4
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• pp.235-243
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• 2019

The discontinuous Galerkin method (DGM) has become widely used as it possesses several qualities, such as a natural ability to dealing with discontinuities. DGM has its major success related to fluid mechanics. Its major importance is the ability to deal with discontinuities and still provide high order of approximation. That is an important advantage when simulating cracking propagation. No remeshing is necessary during the propagation, since the crack path follows the interface of elements. However, DGM comes with the drawback of an increased number of degrees of freedom when compared to the classical continuous finite element method. Thus, it seems a natural approach to combine them in the same simulation obtaining the advantages of both methods. This paper proposes the application of the combined continuous-discontinuous Galerkin method (CDGM) to crack propagation. An important engineering problem is the simulation of crack propagation in concrete structures. The problem is characterized by discontinuities that evolve throughout the domain. Crack propagation is simulated using CDGM. Discontinuous elements are placed in regions with discontinuities and continuous elements elsewhere. The cohesive zone model describes the fracture process zone where softening effects are expressed by cohesive zones in the interface of elements. Two numerical examples demonstrate the capacities of CDGM. In the first example, a plain concrete beam is submitted to a three-point bending test. Numerical results are compared to experimental data from the literature. The second example deals with a full-scale ground slab, comparing the CDGM results to numerical and experimental data from the literature.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.5B
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• pp.475-483
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• 2008

2D finite element model for analysis of transport of accidentally released pollutants in the flow was developed by SUPG method, and the mass balance of this model was checked though two example problems: line source and point source problem in the straight channel and unidirectional 2D flow field, respectively. All the test cases were simulated with both SUPG and conventional Galerkin method to compare the accuraccy of the numerical mass balance. Test results show that the model with SUPG can adequately conserve the released mass though simulation than the model using Galerkin method, so the developed model verified to be appropriate to solve this accidental mass release problem.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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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 Advanced Navigation Technology
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• v.16 no.4
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• pp.635-640
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• 2012

In this paper, The TE (Transverse Electric) scattering problems by a perfectly conducting strip grating over a grounded two dielectric layers are analyzed by applying the conductive boundary condition and the FGMM (Fourier-Galerkin Moment Method) known as a numerical procedure, then the induced surface current density is expanded in a series of the multiplication of the unknown coefficient and the exponential function as a simple function. Generally, the reflected power gets increased according as the relative permittivity ${\epsilon}_{r2}$ and the thickness of dielectric layer $t_2$ of the region-2 in the presented structure gets increased, respectively. The sharp variations of the reflected power are due to resonance effects were previously called wood's anomaly, the numerical results show in good agreement with those of the existing papers.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.12
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• pp.32-40
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• 2018

In order to avoid excessive vibration, it is required to carry out a vibration analysis of heat-exchanger/nuclear-reactor at the design stage. Information of eigen-frequency in the vibration problem is required to evaluate safety of heat-exchange/nuclear reactor. This paper describes a numerical method, Galerkin's method, to solve the eigenvalue problem occurred in a cantilever beam. The beam is restrained with added mass and spring at the free end or a node point of a mode shape. The numerical results of eigen-frequency were compared with simple analytical and experimental results given by simple approach and simple test, respectively. It is found that Galerkin's method is applicable to estimate the eigen-frequency of the cantilever beam. The frequencies become lower with increasing the added mass and the frequencies increase with the spring force. It is shown the heavy added mass has a role of support on the flexible tube. The eigen-frequency of the first mode, for the system with the added mass mounted at the free end, can be calculated by the approximate analytical method existing with more or less accuracy.

• Coupled systems mechanics
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• v.5 no.3
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• pp.203-221
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• 2016

The present study deals with the numerical modelling for the one dimensional contaminant transport through saturated homogeneous and stratified porous media using meshfree method. A numerical algorithm based on element free Galerkin method is developed. A one dimensional form of the advectivediffusive transport equation for homogeneous and stratified soil is considered for the analysis using irregular nodes. A Fortran program is developed to obtain numerical solution and the results are validated with the available results in the literature. A detailed parametric study is conducted to examine the effect of certain key parameters. Effect of change of dispersion, velocity, porosity, distribution coefficient and thickness of layer is studied on the concentration of the contaminant.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.267-280
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• 2009

In this paper we investigate a simple two-level additive Schwarz preconditioner for the P1 symmetric interior penalty Galerkin method of the Poisson equation on rectangular meshes. The construction is based on the decomposition of the global space of piecewise linear polynomials into the sum of local subspaces, each of which corresponds to an element of the underlying mesh, and the global coarse subspace consisting of piecewise constants. This preconditioner is a direct combination of the block Jacobi iteration and the cell-centered finite difference method, and thus very easy to implement. Explicit upper and lower bounds for the maximum and minimum eigenvalues of the preconditioned matrix system are derived and confirmed by some numerical experiments.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.131-134
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• 2005

Conventional high order interpolation schemes are limitative in several aspects mainly because they need data of neighboring cells at the reconstruction step. However, discontinuous Galerkin method and spectral volume method, two high order flux schemes which will be analyzed and compared in this paper, have an important benefit that they are not necessary to determine the flow gradients from data of neighboring cells or elements. These two schemes construct polynomial of variables within a cell so that even near wall or discontinuity, the high order does not deteriorate.