• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2001.04a
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• pp.77-80
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• 2001

The element-free Galerkin (EFG) method is one of meshless methods, which is an efficient method of modeling problems of fluid or solid mechanics with complex boundary shapes and large changes in boundary conditions. This paper discusses the theory of the EFG method and its applications to modeling of groundwater flow. In the EFG method, shape functions are constructed based on the moving least square (MLS) approximation, which requires only set of nodes. The EFG method can eliminate time-consuming mesh generation procedure with irregular shaped boundaries because it does not require any elements. The coupled EFG-FEM technique was introduced to treat Dirichlet boundary conditions. A computer code EFGG was developed and tested for the problems of steady-state and transient groundwater flow in homogeneous or heterogeneous aquifers. The accuracy of solutions by the EFG method was similar to that by the FEM. The EFG method has the advantages in convenient node generation and flexible boundary condition implementation.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.10
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• pp.2667-2677
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• 1995

A new numerical algorithm using equal order linear finite element and fractional step method has been developed which is capable of analyzing unsteady fluid flow and heat transfer problems. Streamline Upwind Petrov-Galerkin (SUPG) method is used for the weighted residual formulation of the Navier-Stokes equations. It is shown that fractional step method, in which pressure term is splitted from the momentum equation, reduces computer memory and computing time. In addition, since pressure equation is derived without any approximation procedure unlike in the previously developed SIMPLE algorithm based FEM codes, the present numerical algorithm gives more accurate results than them. The present algorithm has been applied preferentially to the well known bench mark problems associated with steady flow and heat transfer, and proves to be more efficient and accurate.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.4
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• pp.27-35
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• 1991

This paper presents a numerical analysis procedure and a characteristics for vibration and buckling of the cylinderical panels. The panels with simply-simply or simply-clamped edge supports are subjectes to circumferential compressive or flexural stresses. The differential equations governing vibration and buckling for these panels are derived by using the fundamental differential equation of the Love-Timoshenko and are solved numerically via the Galerkin method. The panel with simply-clamped edge supports is used a trigonometric function or a eigen function of a beam as a trial function and the effects of trial functions on numerical solutions are displayed. Numerical results are presented to demonstrate the effects of the flexural parameters in natural frequencies and coefficients of critical buckling and some typical mode shapes of vibration and buckling are also presented.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.4
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• pp.485-500
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• 2000

In this paper the adaptive crack propagation analysis based on the estimated local and global error in the element-free Galerkin (EFG) method is presented. It is possible to keep consistency and accuracy of analysis in each propagation step by adaptive analysis. The adaptivity analysis in crack propagation is achieved by adding and removing the node along the background integration cell that are refined or recovered as estimated error. These errors are obtained by calculating the difference between the values of the projected stresses and original EFG stresses. To evaluate the performance of proposed adaptive procedure, the convergence behavior is investigated lot several examples. The results of these examples show the efficiency of proposed scheme in crack propagation analysis.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.4
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• pp.525-535
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• 2001

In this paper, a new adaptive analysis scheme for element-free Galerkin method(EFGM) is proposed. The novel point of this scheme is that the triangular cell structure based on the Delaunay triangulation is used in the numerical integration and the node adding/removing process. In adaptive analysis with this scheme, there is no need to divide the integration cell and the memory cell structure. For the adaptive analysis of crack propagation, the reconstruction of cell structure by adding and removing the nodes on integration cells based the estimated error should be carried out at every iteration step by the Delaunay triangulation technique. This feature provides more convenient user interface that is closer to the real mesh-free nature of EFGM. The analysis error is obtained basically by calculating the difference between the values of the projected stresses and the original EFG stresses. To evaluate the performance of proposed adaptive procedure, the crack propagation behavior is investigated for several examples.

• 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 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.

• Journal of Korean Society of Steel Construction
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• v.12 no.6
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• pp.737-748
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• 2000

This paper presents a numerical analysis procedure and a characteristics for dynamic of cylindrical panels. The panels with simply-simply or simply-clamped edge supports are subjectes to circumferential compressive or flexural stresses. The differential equations governing vibration and dynamic for these panels are derived by using the fundamental differential equation of the Love-Timoshenko and are solved numerically by the Galerkin method. The panel with simply-clamped edge supports is used a trigonometric function or an eigen function of a beam as a trial function and the effects of trial functions on numerical solutions are displayed. Numerical results are presented to demonstrate the effects of the flexural parameters in natural frequencies and coefficients of critical buckling, and some typical mode shapes of vibration and buckling are also presented.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.371-378
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• 2000

In this study an adaptive node generation procedure in the Element-free Galerkin (EFG) method using bubble-meshing technique is proposed. Based on the error function that obtained by projected error estimation method, the initial node arrangement is defined along the background cell that is used in the numerical integration. To obtain the smooth nodal configuration, the nodal configuration are regenerated by bubble-meshing technique. This bubble meshing technique was originally developed to generate a set of well-shaped triangles and tetrahedra. Its basic idea is packing circles or spheres, called bubble, into the specified area or space naturally using some dynamic equations with attracting and repelling force. To demonstrate the performance of proposed scheme, the convergence behaviors are investigated for several problems.

• Nuclear Engineering and Technology
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• v.41 no.8
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• pp.1087-1100
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• 2009

A finite element method utilizing the Galerkin form of the weighted residuals procedure was developed to estimate the mechanical behavior for a coated fuel particle (CFP) of a high temperature gas-cooled reactor (HTGR). Through a weak formulation, finite element equations for multiple layers were set up to calculate the displacements and stresses in a CFP. The finite element method was applied to the stress analyses for three coating layers of a tri-isotropic coated fuel particle (TRISO) of a HTGR. The stresses calculated by the finite element method were in good agreement with those from a previously developed computer code and depicted the typical stress behavior of the coating layers very well. The newly developed finite element method performs a stress analysis for multiple bonded layers in a CFP by changing the material properties at any position in the layers during irradiation.