• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.95-104
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• 2007

We study stationary subdivision schemes based on radial basis function interpolation. Each scheme has a tension parameter, say ${\lambda}$, which actually belongs to the radial basis function. In particular, adapted subdivision rules on bounded intervals are developed.

• Structural Engineering and Mechanics
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• 제15권5호
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• pp.535-550
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• 2003

In this paper, a boundary-type meshfree method, the boundary radial point interpolation method (BRPIM), is presented for solving boundary value problems of two-dimensional solid mechanics. In the BRPIM, the boundary of a problem domain is represented by a set of properly scattered nodes. A technique is proposed to construct shape functions using radial functions as basis functions. The shape functions so formulated are proven to possess both delta function property and partitions of unity property. Boundary conditions can be easily implemented as in the conventional Boundary Element Method (BEM). The Boundary Integral Equation (BIE) for 2-D elastostatics is discretized using the radial basis point interpolation. Some important parameters on the performance of the BRPIM are investigated thoroughly. Validity and efficiency of the present BRPIM are demonstrated through a number of numerical examples.

• Structural Engineering and Mechanics
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• 제14권6호
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• pp.713-732
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• 2002

A local radial point interpolation method (LRPIM) based on local residual formulation is presented and applied to solid mechanics in this paper. In LRPIM, the trial function is constructed by the radial point interpolation method (PIM) and establishes discrete equations through a local residual formulation, which can be carried out nodes by nodes. Therefore, element connectivity for trial function and background mesh for integration is not necessary. Radial PIM is used for interpolation so that singularity in polynomial PIM may be avoided. Essential boundary conditions can be imposed by a straightforward and effective manner due to its Delta properties. Moreover, the approximation quality of the radial PIM is evaluated by the surface fitting of given functions. Numerical performance for this LRPIM method is further studied through several numerical examples of solid mechanics.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.495-500
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• 2007

A Meshfree is a method used to establish algebraic equations of system for the whole problem domain without the use of a predefined mesh for the domain discretization. A point interpolation method is based on combining radial and polynomial basis functions. Involvement of radial basis functions overcomes possible singularity. Furthermore, the interpolation function passes through all scattered points in an influence domain and thus shape functions are of delta function property. This makes the implementation of essential boundary conditions much easier than the meshfree methods based on the moving least-squares approximation. This study aims to investigate a stress analysis of structural element between a meshfree method and the finite element method. Examples on cantilever type plate and stress concentration problems show that the accuracy and convergence rate of the meshfree methods are high.

• 한국측량학회지
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• 제23권1호
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• pp.39-47
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• 2005

본 연구에서는 오늘날 해상측량에서 주로 사용되고 있는 DGPS기법과 음향측심기를 조합하여 취득된 해저지형의 3차원 위치정보를 크리깅(kriging), RBF(radial basis function), 최근린(nearest neighbor) 보간법을 이용하여, 항만공사에서의 호퍼준설량을 산정하였다. 또한, 각각의 보간법에 의해 산정된 호퍼준설량과 실제 준설량을 비교·분석함으로써, 준설량 산정에 있어 DGPS/Echo Sounder 기법의 활용성을 확인할 수 있었다. 그 결과, 크리깅 보간법을 적용한 경우 내용적 차이는 15,364㎥로 약 1.89%의 오차율을 나타내었으며, RBF 보간법과 최근린 보간법을 적용한 경우에는 각각 3.9%, 4.4%의 오차율을 나타내었다. 향후, 항만공사에서의 준설량 산정에 있어서 해저지형의 특성에 따른 적합한 보간법 적용에 관련한 연구가 선행될 경우, 보다 신속하고 정확한 준설량을 산정 할 수 있을 것으로 기대된다.

• Geomechanics and Engineering
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• 제2권2호
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• pp.141-156
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• 2010

In the framework of meshfree methods, a new methodology is developed based on radial point interpolation method (RPIM). This methodology is applied to a one-dimensional contaminant transport modelling in the saturated porous media. The one-dimensional form of advection-dispersion equation involving reactive contaminant is considered in the analysis. The Galerkin weak form of the governing equation is formulated using 1D meshfree shape functions constructed using thin plate spline radial basis functions. MATLAB code is developed to obtain the numerical solution. Numerical examples representing various phenomena, which occur during migration of contaminants, are presented to illustrate the applicability of the proposed method and the results are compared with those obtained from the analytical and finite element solutions. The proposed RPIM has generated results with no oscillations and they are insensitive to Peclet constraints. In order to test the practical applicability and performance of the RPIM, three case studies of contaminant transport through the landfill liners are presented. A good agreement is obtained between the results of the RPIM and the field investigation data.

• 한국지리정보학회지
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• 제13권3호
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• pp.29-41
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• 2010

본 연구는 미측정점의 값을 모델링하기 위해 사용되는 여러 가지 공간보간방법들의 예측오차를 비교하고 정확성을 검증하였다. 동해안 해안 지역의 표고점을 대상으로 역거리가중법, 크리깅, 지역 다항식보간법, 방사기반함수의 공간보간법과 관련된 매개변수들을 동일한 조건하에서 실행하여 평균제곱근을 산출한 결과, 단순 크리깅 방법의 원형 모델이 가장 작은 값으로 나타났다. 래스터의 연산 결과, 방사기반함수의 다중방정식에 의한 예측 지도가 대상 지역의 불규칙삼각망 표현과 일치정도가 높았다. 또한 공간보간 실행시 선택된 조건하에서 제공되는 최적 파워값을 사용하는 것이 양호한 보간 결과를 얻을 수 있다.

• 한국전산구조공학회논문집
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• 제20권3호
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• pp.311-319
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• 2007

본 연구에서는 구조 요소의 응력해석을 위한 무요소 RPIM(Meshfree Radial Point Interpolation Methods)법을 제시한다. 이를 위하여 먼저 무요소법의 형상함수와 무요소 RPIM법의 정식화 과정 및 프로그래밍을 간략히 한다. 절점보간법은 방사기저함수와 다항기저함수를 포함하고 있고 이 중 다항기저함수는 특이성문제를 극복할 수 있다. 게다가 무요소 RPIM법의 보간함수는 영향영역의 절점을 통과하고 형상함수는 크로네커 델타 성질을 갖고 있으므로 최소자승법에 기반을 둔 무요소법보다 쉽게 필수경계조건을 만족시킨다. 본 연구의 정확성을 확인하기 위하여, 캔틸레버형 평판, 유공평판, 속이 빈 원통 문제의 수치예제를 수행하고 이론 해와 유한요소법 결과를 비교, 분석한다.

• 한국지능시스템학회논문지
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• 제7권3호
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• pp.89-95
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• 1997

This paper examines the relation between multidimensional linear interpolation (MDI) and regularization net-works, and shows that an MDI is a special form of regularization networks. For this purpose we propose a triangular basis function(TBF) network. Also we verified the condition when our proposed TBF becomes a well-known radial basis function (RBF).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.321-332
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• 2010

In this paper, we experiment image warping and morphing. In image warping, we use radial basis functions : Thin Plate Spline, Multi-quadratic and Gaussian. Then we obtain the fact that Thin Plate Spline interpolation of the displacement with reverse mapping is the efficient means of image warping. Reflecting the result of image warping, we generate two examples of image morphing.