• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.615-622
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• 2002

In this paper, the modification of double projection method for the adaptive analysis of Element-free Galerkin(EFG) method were proposed. As results of the double projection method, the smoothed error profile that is adequate for adaptive analysis was obtained by re-projection of error that means the differences of EFG stress and projected stress. However, it was found that the efficiency of double projection method is degraded as increase of the numerical integration order. Since, the iterative refinement to single step error estimation made the same effect as increasing of integration order, the application of the iterative refinement base on double projection method could be produced the inadequately refined analysis model. To overcome this defect, a modified scheme of double projection were proposed. In the numerical example, the results did not show degradation of double projection effect in iterative refinement and the efficiency of proposed scheme were proved.

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.4
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• pp.37-44
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• 1987

In order to perform a detailed analysis of large deflection behaviour of a rectangular plate, an efficient semi-analytical method is developed in this paper. The method is called Incremental Galerkin Method. This method is successfully applied to plates with initial deflection subjected to in-plane and out-of-plane loads to obtain the whole histories of the behaviour of these plates. Application of this method to rectangular plates with initial deflection is presented. Comparisons of results obtained by this method with those obtained by other methods are made and the validity of the method is demonstrated.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.419-431
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• 2023

In this paper, we propose an iterative method for a symmetric interior penalty Galerkin method for heterogeneous elliptic problems. The iterative method consists mainly of two parts based on a non-overlapping domain decomposition approach. One is an intermediate preconditioner constructed by understanding the properties of the discontinuous finite element functions and the other is a preconditioning related to the dual-primal finite element tearing and interconnecting (FETI-DP) methodology. Numerical results for the proposed method are presented, which demonstrate the performance of the iterative method in terms of various parameters associated with the elliptic model problem, the finite element discretization, and non-overlapping subdomain decomposition.

• Steel and Composite Structures
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• v.24 no.5
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• pp.523-536
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• 2017

A layerwise (LW) formulation based on the Galerkin method is presented to investigate the three-dimensional stress state in long sandwich plate which is subjected to tension force and pure bending moment. Based on the Galerkin method and the LW discretization approach, the equilibrium equations of elasticity for the long plate are written in the weak form and discretized through the thickness of the plate. The discretized equations are written in terms of displacement components of the numerical layers. The governing equations of the plate are solved analytically for the free edge boundary conditions. The distribution of stress state especially the 3D stress state in the vicinity of the edges of the sandwich plate which is subjected to tension and pure bending is studied. In order to increase the accuracy, the out of plane stresses are obtained by integrating the equilibrium equations of elasticity. The convergence and accuracy of the predictions are studied and various numerical results are presented for distribution of the in-plane and out of plane stresses in symmetric and un-symmetric sandwich plates.

• Structural Engineering and Mechanics
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• v.35 no.4
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• pp.387-407
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• 2010

In this paper, using perturbation and Galerkin method, the response of a resonant viscoelastic microbeam to an electric actuation is obtained. The microbeam is under axial load and electrical load. It is assumed that midplane is stretched, when the beam is deflected. The equation of motion is derived using the Newton's second law. The viscoelastic model is taken to be the Kelvin-Voigt model. In the first section, the static deflection is obtained using the Galerkin method. Exact linear symmetric mode shape of a straight beam and its deflection function under constant transverse load are used as admissible functions. So, an analytical expression that describes the static deflection at all points is obtained. Comparing the result with previous research show that using deflection function as admissible function decreases the computation errors and previous calculations volume. In the second section, the response of a microbeam resonator system under primary and secondary resonance excitation has been obtained by analytical multiple scale perturbation method combined with the Galerkin method. It is shown, that a small amount of viscoelastic damping has an important effect and causes to decrease the maximum amplitude of response, and to shift the resonance frequency. Also, it shown, that an increase of the DC voltage, ratio of the air gap to the microbeam thickness, tensile axial load, would increase the effect of viscoelastic damping, and an increase of the compressive axial load would decrease the effect of viscoelastic damping.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.10B
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• pp.1885-1894
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• 1999

The higher mode cutoff frequencies in Crawford TEM cells computed by the Galerkin method(GM) describe in this paper. The authors also report the half mode boundaries to solve not only the cut-off frequencies of symmetric TEM cells and those of asymmetric TEM cells. It is shown that the measured resonant frequencies of the present symmetric TEM cells and a designed asymmetric TEM cell are agreed with the calculated results.

• The Journal of the Acoustical Society of Korea
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• v.18 no.4
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• pp.71-77
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• 1999

Exact forward modeling of acoustic propagation is crucial in MFP such as inverse problems and various other acoustic applications. As acoustic propagation in shallow water environments become important, range dependent modeling has to be considered of which PE method is considered as one of the most accurate and relatively fast. In this paper higher order numerical rode employing the PE method is developed. To approximate the depth directional operator, Galerkin's method is used with partial collocation to lessen necessary calculations. Linearization of tile depth directional operator is achieved via expansion into a multiplication form of (equation omitted) approximation. To approximate the range directional equation, Crank-Nicolson's method is used. Final1y, numerical self stater is employed. Numerical tests are performed for various occan environment scenarios. The results of these tests are compared to exact solutions, OASES and RAM results.

• Journal of Mechanical Science and Technology
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• v.17 no.1
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• pp.64-76
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• 2003

In this work, a new penalty formulation is proposed for the analysis of Mindlin-Reissner plates by using the element-free Galerkin method. A penalized weak form for the Mindlin-Reissner Plates is constructed through the exterior penalty method to enforce the essential boundary conditions of rotations as well as transverse displacements. In the numerical examples, some typical problems of Mindlin-Reissner plates are analyzed, and parametric studies on the order of integration and the size of influence domain are also carried out. The effect of the types of background cells on the accuracy of numerical solutions is observed and a proper type of background cell for obtaining optimal accuracy is suggested. Further, optimal order of integration and basis order of Moving Least Squares approximation are suggested to efficiently handle the irregularly distributed nodes through the triangular type of background cells. From the numerical tests, it is identified that unlike the finite element method, the proposed element-free Galerkin method with penalty technique gives highly accurate solution without shear locking in dealing with Mindlin-Reissner plates.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.333-340
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• 2004

This paper deals with geometric nonlinear analyses using a new meshfree technique which improves the numerical integration accuracy. The new method called the Petrov-Galerkin natural element method (PGNEM) is based on the Voronoi diagram and the Delaunay triangulation which is based on the same concept used for conventional natural element method called the Bubnov-Galerkin natural element method (BGNEM). But, unlike BGNEM, the test shape function is differently chosen from the trial shape function. In the linear static analysis, it is ensured that the numerical integration error of the PGNEM is remarkably reduced. In this paper, the PGNEM is applied to large deformation problems, and the accuracy of the proposed numerical technique is verified through the several examples.