• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.599-603
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• 2002

We propose a new meshfree method to be called the fast moving least square reproducing kernel collocation method(FCM). This methodology is composed of the fast moving least square reproducing kernel(FMLSRK) approximation and the point collocation scheme. Using point collocation makes the meshfree method really come true. In this paper, FCM Is shown to be a good method at least to calculate the numerical solutions governed by second order elliptic partial differential equations with geometric singularity or geometric multi-scales. To treat such problems, we use the concept of variable dilation parameter.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.23 no.4
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• pp.385-392
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• 2005

This paper describes an accuracy analysis of newly developed gravimetric geoid and an improvement of developed geoid using GPS/Levelling data. We developed the KGEOID05 model corrected with the correction term. The correction term is modelled using the difference between GPS/Levelling derived geoidal heights and gravimetric geoidal heights. The stochastic model used in the calculation of correction term is the least squares collocation technique based on second-order Markov covariance function. 373 GPS stations were used to model the correction term. The standard deviation of KGEOID05 is about 11 cm and it indicates that we can be determined accurate heights ($2{\sim}3\;cm$) when we made precise modelling using KGEOID05 and a few GPS measurements for the local area.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• v.4B no.4
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• pp.180-183
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• 2004

This paper presents a description of the point collocation method and its application to the electromagnetic field computation. The interpolation scheme is based on the fast moving least square reproducing kernel approximation. In the method, the integration cell is not required and the essential boundary conditions can be enforced directly. Numerical simulations on 1-D and 2-D problems are carried out to validate the method. It is found that computational efficiency is higher than the general mesh-free methods.

• Structural Engineering and Mechanics
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• v.17 no.5
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• pp.671-690
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• 2004

A meshless method with novel variation of point collocation by finite mixture approximation is developed in this paper, termed the meshless finite mixture (MFM) method. It is based on the finite mixture theorem and consists of two or more existing meshless techniques for exploitation of their respective merits for the numerical solution of partial differential boundary value (PDBV) problems. In this representation, the classical reproducing kernel particle and differential quadrature techniques are mixed in a point collocation framework. The least-square method is used to optimize the value of the weight coefficient to construct the final finite mixture approximation with higher accuracy and numerical stability. In order to validate the developed MFM method, several one- and two-dimensional PDBV problems are studied with different mixed boundary conditions. From the numerical results, it is observed that the optimized MFM weight coefficient can improve significantly the numerical stability and accuracy of the newly developed MFM method for the various PDBV problems.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1737-1751
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• 2013

An efficient and stable point collocation scheme based on a meshfree method is studied for the stationary incompressible Navier-Stokes equations. We describe the diffuse derivatives associated with the moving least square method. Using these diffuse derivatives, we propose a point collocation method to fit in solving the Navier-Stokes equations which improves the stability of the direct point collocation scheme. The convergence of the numerical solution is investigated from numerical examples. The driven cavity ow and the backward facing step ow are implemented for the reliability of the scheme. Also, the viscous ow on complicated geometry is successfully calculated such as the ow past a circular cylinder in duct.

• Communications of the Korean Mathematical Society
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• v.6 no.1
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• pp.47-54
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• 1991

• 한국정보통신설비학회:학술대회논문집
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• 2008.08a
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• pp.190-192
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• 2008

This paper shows the formulation of fast moving least square reproducing kernel method (FMLSRKM) which is a kind of meshfree methods. FMLSRKM has some advantages compared to conventional numerical techniques such as finite element method. For simple analysis on a rectangular waveguide, point collocation scheme is introduced and applied.

• Korean Journal of Geomatics
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• v.5 no.1
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• pp.21-26
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• 2005

According to revisions of survey law taking effect on January 1, 2003, the Korean geodetic datum has been changed from a local geodetic to a world geodetic system. In this study, the datum transformation parameters especially for the maritime geographical data are determined. From database constructed through MGIS, a total of 492 coordinate pairs were selected and used in the parameter determination after outlier testing. Based on the parameter estimation, the Molodensky model is selected for datum transformation. For higher accuracy, Application of network optimization and a least squares collocation with Gaussian model has resulted in the accuracy better than 15 cm in coordinate transformation.

• Journal of computational fluids engineering
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• v.14 no.4
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• pp.93-100
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• 2009

The gridless (or meshfree) methods, such as MPS, SPH, FPM an so forth, are feasible and robust for the problems with moving boundary and/or complicated boundary shapes, because these methods do not need to generate a grid system. In this study, a gridless solver, which is based on the combination of moving least square interpolations on a cloud of points with point collocation for evaluating the derivatives of governing equations, is presented for two-dimensional unsteady incompressible Navier-Stokes problem in the low Reynolds number. A MAC-type algorithm was adopted and the Poission equation for the pressure was solved successively in the moving least square sense. Some typical problems were solved by the presented solver for the validation and the results obtained were compared with analytic solutions and the numerical results by conventional CFD methods, such as a FVM.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.6
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• pp.895-903
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• 1987

This paper investigates the problem of cracks emanating from a circular hole in an orthotropic infinite plate. The mixed-mode stress intensity factors are obtained by using the modified mapping-collocation method. To investigate the effect of anisotropy and circular hole boundary on crack tip singularity, stress intensity factors are considered as functions of the normalized crack length for various types of laminated composite. The results indicate a strong dependence of the stress intensity factor on the material anisotropy and geometry.