• Journal of the Korean Mathematical Society
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• v.29 no.2
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• pp.225-238
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• 1992

• 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.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.23 no.4
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• pp.541-550
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• 2012

An improved method of moments using a hybrid Galerkin-interpolation technique for numerical analysis of electromagnetic wave scattering in the 3-dimensional space is presented in this paper. Basically, the EFIE(electric field integral equation) and RWG(Rao-Wilton-Glisson) basis function are used to compute a property of electromagnetic wave scattering. We propose a hybrid technique combining the existing Galerkin's method with the interpolation method to improve the efficiency of the numerical computation. Then, an index of relative distance of each cells was defined to distinguish the relatively far elements, which interpolation method can be applied. To verify the performance of the proposed technique, the analytical Mie-series solution was used to compute the theoretical RCS of a conducting sphere for the purpose of comparison. We also applied this hybrid technique to various scatterers such as trihedral/omni-directional corner-reflectors to analyze the radar backscattering properties.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.10
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• pp.1605-1612
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• 2001

Least-squares meshfree method is presented. Conventional meshfree methods based on the Galerkin formulation suffer from inaccurate numerical integration. Least-squares formulation exhibits rather different integration-related characteristics. It is demonstrated through numerical examples that least-squares formulation is much more robust to integration errors than the Galerkin's. Therefore efficient meshfree methods can be devised by combining very simple integration algorithms and least-squares formulation.

• Computers and Concrete
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• v.16 no.5
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• pp.669-682
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• 2015

Degradation of reinforced concrete (RC) structures due to chloride penetration followed by reinforcement corrosion has been a serious problem in civil engineering for many years. The numerical simulation methods at present are mainly finite element method (FEM) and finite difference method (FDM), which are based on mesh. Mesh generation in engineering takes a long time. In the present article, the numerical solution of chloride transport in concrete is analyzed using radial point interpolation method (RPIM) and element-free Galerkin (EFG). They are all meshless methods. RPIM utilizes radial polynomial basis, whereas EFG uses the moving least-square approximation. A Galerkin weak form on global is used to attain the discrete equation, and four different numerical examples are presented. MQ function and appropriate parameters have been proposed in RPIM. Numerical simulation results are compared with those obtained from the finite element method (FEM) and analytical solutions. Two case of chloride transport in full saturated and unsaturated concrete are analyzed to test the practical applicability and performance of the RPIM and EFG. A good agreement is obtained among RPIM, EFG, and the experimental data. It indicates that RPIM and EFG are reliable meshless methods for prediction of chloride concentration in concrete structures.

• Journal of computational fluids engineering
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• v.21 no.2
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• pp.1-11
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• 2016

Considerable efforts are required to develop a monotone, robust and stable high-order numerical scheme for solving the hyperbolic system. The discontinuous Galerkin(DG) method is a natural choice, but elimination of the spurious oscillations from the high-order solutions demands a new development of proper limiters for the DG method. There are several available limiters for controlling or removing unphysical oscillations from the high-order approximate solution; however, very few studies were directed to analyze the exact role of the limiters in the hyperbolic systems. In this study, the performance of the several well-known limiters is examined by comparing the high-order($p^1$, $p^2$, and $p^3$) approximate solutions with the exact solutions. It is shown that the accuracy of the limiter is in general problem-dependent, although the Hermite WENO limiter and maximum principle limiter perform better than the TVD and generalized moment limiters for most of the test cases. It is also shown that application of the troubled cell indicators may improve the accuracy of the limiters under some specific conditions.

• Structural Engineering and Mechanics
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• v.56 no.4
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• pp.589-603
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• 2015

The mixed-mode stress intensity factors of 2-D angled cracks are evaluated by Petrov-Galerkin natural element (PG-NE) method in which Voronoi polygon-based Laplace interpolation functions and CS-FE basis functions are used for the trial and test functions respectively. The interaction integral is implemented in a frame of PG-NE method in which the weighting function defined over a crack-tip integral domain is interpolated by Laplace interpolation functions. Two Cartesian coordinate systems are employed and the displacement, strains and stresses which are solved in the grid-oriented coordinate system are transformed to the other coordinate system aligned to the angled crack. The present method is validated through the numerical experiments with the angled edge and center cracks, and the numerical accuracy is examined with respect to the grid density, crack length and angle. Also, the stress intensity factors obtained by the present method are compared with other numerical methods and the exact solution. It is observed from the numerical results that the present method successfully and accurately evaluates the mixed-mode stress intensity factors of 2-D angled cracks for various crack lengths and crack angles.

• Ocean Systems Engineering
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• v.3 no.4
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• pp.327-348
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• 2013

An Oscillating Water Column (OWC) is a relatively practical and convenient device that converts wave energy to a usable form, which is electricity. The OWC is kept inside a fixed truncated vertical cylinder, which is a hollow structure with one open end submerged in the water and with an air turbine at the top. This research adopts potential theory and Galerkin methods to solve the fluid motion inside the OWC. Using an air-water interaction model, OWC design for energy extraction from regular wave is also explored. The hydrodynamic coefficients of the scattering and radiation potentials are solved for using the Galerkin approximation. The numerical results for the free surface elevation have been verified by a series of experiments conducted in the University of New Orleans towing tank. The effect of varying geometric parameters on the response amplitude operator (RAO) of the OWC is studied and modification of the equation for evaluating the natural frequency of the OWC is made. Using the model of air-water interaction under certain wave parameters and OWC geometric parameters, a computer program is developed to calculate the energy output from the system.

• International Journal of CAD/CAM
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• v.8 no.1
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• pp.1-10
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• 2009

This paper presents a topology optimization approach using element-free Galerkin method (EFGM) for the optimal design of compliant mechanisms with geometrically non-linearity. Meshless method has an advantage over the finite element method(FEM) because it is more capable of handling large deformation resulted from geometrical nonlinearity. Therefore, in this paper, EFGM is employed to discretize the governing equations and the bulk density field. The sensitivity analysis of the optimization problem is performed by incorporating the adjoint approach with the meshless method. The Lagrange multipliers method adjusted for imposition of both the concentrated and continuous essential boundary conditions in the EFGM is proposed in details. The optimization mathematical formulation is developed to convert the multi-criteria problem to an equivalent single-objective problem. The popularly applied interpolation scheme, solid isotropic material with penalization (SIMP), is used to indicate the dependence of material property upon on pseudo densities discretized to the integration points. A well studied numerical example has been applied to demonstrate the proposed approach works very well and the non-linear EFGM can obtain the better topologies than the linear EFGM to design large-displacement compliant mechanisms.