• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 가을 학술발표회 논문집
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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.

• 한국측량학회지
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• 제23권4호
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• pp.385-392
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• 2005

본 논문에서는 중력데이터를 사용하여 중력지오이드모델을 개발하고, GPS/Leveling데이터를 사용하여 개선한 KGEOID05모델을 계산하였으며, 그 정밀도를 분석하였다. KGEOID05는 중력지오이드모델에 보정항을 더하여 계산하였으며, 보정항은 GPS/Levelling에 의하여 구한 지오이드고와 중력지오이드고의 차이를 사용하여 모델링 하였다. 모델링을 위한 통계학적 함수는 Markov 2차공분산 함수에 기초한 least squares collocation방법을 사용하였다. 총 373점의 GPS관측점을 보정항 모델링에 사용하였으며, 정밀도분석결과 KGEOID05의 정밀도는 11cm로 계산되었다. $2{\sim}3$점의 수준점에 대한 GPS관측데이터를 사용하여 지역적으로 KGEOID05모델에 대한 fitting을 실시할 경우에 GPS관측에 의한 $2{\sim}3cm$ 정밀도의 표고측정이 가능하다.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• 제4B권4호
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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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• 제17권5호
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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.

• 대한수학회보
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• 제50권5호
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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.

• 대한수학회논문집
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• 제6권1호
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• pp.47-54
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• 1991

• 한국정보통신설비학회:학술대회논문집
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• 한국정보통신설비학회 2008년도 정보통신설비 학술대회
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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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• 제5권1호
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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.

• 한국전산유체공학회지
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• 제14권4호
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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.

• 대한기계학회논문집
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• 제11권6호
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• pp.895-903
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• 1987

본 연구에서는 참고문헌 (16)과 (17)에서 등방성과 이방성에 각각 처음으로 제시한 수정 사상 선점법(modified mapping-collocation method)을 이용해서 직교 이 방성 무한 평판 내부의 원공 주위 균열 문제에 대한 혼합모우드 응력 강도 계수를 구 하고자 한다. 본 문제는 기하학적으로 복잡하고 재료의 이방성이 강하기 때문에 해 가 아직 보고되어 있지 않다. 먼저 이론적 해석을 전개함으로써 규열 면에서의 무부 하 조건과 무한점에서의 경계 조건을 완전하게 만족시킨다. 그 후 나머지 원공 경계 에 최소 자승 선점 과정(least square collocation procedure)을 적용하여 근사해를 얻게 된다. 균열 선단 응력 특이성에 미치는 원공 경계 및 이방성의 효과를 알아보 기 위해서 여러가지 형태의 적층판에 대한 응력 강도 계수를 무차원화된 균열 길이의 함수로 나타내 보았다.