• 전기학회논문지
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• 제68권1호
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• pp.83-89
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• 2019

In this paper, beam forming using moving least squares method (MLSM) is studied. In the previous research, the least squares method (LSM), one of the data interpolation methods, was used to determine the desired beam pattern and obtain a beam pattern that minimizes the square of the error with the desired beam pattern. However, LSM has a disadvantage in that the beam pattern can not be formed to satisfy the exact steering angle of the desired beam pattern and the peak sidelobe level (PSLL) condition. To overcome this drawback, MLSM is used for beam forming. In order to verify, the proposed method is applied in beam forming of Bezier platform array antenna which is one of conformal array antenna platform.

• 대한기계학회논문집A
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• 제30권12호
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• pp.1626-1633
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• 2006

In the present paper, in the context of the meshless interpolation of a moving least squares (MLS) type, a novel method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order to improve the accuracy of solution. The secondary nodes can be placed at any location where one needs to obtain a better resolution. The support domains for the shape functions in the MLS approximation are defined from the primary nodes, and the secondary nodes use the same support domains. The shape functions based on the MLS approximation, in an integration domain, have a single type of a rational function, which reduces the difficulty of numerical integration to evaluate the weak form. The present method is very useful in an adaptive calculation, because the secondary nodes can be easily added and moved without an additional mesh. Several numerical examples are presented to illustrate the effectiveness of the present method.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 가을 학술발표회 논문집
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• pp.591-598
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• 2002

The interface element method for non-matching FEM meshes is extended using stabilized nodal integration. Two non-matching meshes are shown to be joined together compatibly, with the aid of the moving least square approximation. Using stabilized nodal integration, the interface element method is able to satisfy the patch test, which guarantees the convergence of the method.

• 한국지하수토양환경학회:학술대회논문집
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• 한국지하수토양환경학회 2001년도 총회 및 춘계학술발표회
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• pp.77-80
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• 2001

The element-free Galerkin (EFG) method is one of meshless methods, which is an efficient method of modeling problems of fluid or solid mechanics with complex boundary shapes and large changes in boundary conditions. This paper discusses the theory of the EFG method and its applications to modeling of groundwater flow. In the EFG method, shape functions are constructed based on the moving least square (MLS) approximation, which requires only set of nodes. The EFG method can eliminate time-consuming mesh generation procedure with irregular shaped boundaries because it does not require any elements. The coupled EFG-FEM technique was introduced to treat Dirichlet boundary conditions. A computer code EFGG was developed and tested for the problems of steady-state and transient groundwater flow in homogeneous or heterogeneous aquifers. The accuracy of solutions by the EFG method was similar to that by the FEM. The EFG method has the advantages in convenient node generation and flexible boundary condition implementation.

• 대한수학회지
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• 제43권5호
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• pp.1081-1098
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• 2006

Mathematical analysis is made on a mesh free method for the compressible Euler equations. In particular, the Moving Least Square Reproducing Kernel (MLSRK) method is employed for space approximation. With the backward-Euler method used for time discretization, existence of discrete solution and it's $L^2-error$ estimate are obtained under a regularity assumption of the continuous solution. The result of numerical experiment made on the biconvex airfoil is presented.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 가을 학술발표회 논문집
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• pp.567-574
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• 2002

새로운 자유격자 관사를 이용한 점별 계산법을 제안한다 이동 최소 자승법을 이용한 기저의 생성과 기저의 근사적 미분을 동시에 구해내는 자유격자 근사를 유도하여, 직접 점별 계산법을 고안하였다. 기존의 자유 격자 법에서는 기저의 직접 미분을 사용하므로 높은 계산 비용이 필요하지만, 이 논문에서 제안된 방법은 기저의 생성과 동시에 기저의 근사적 미분을 구하게 된다. 또한 기존의 방법에서 필요하였던, 창 함수(window function)의 미분가능성을 연속성으로 대치할 수 있으므로, 주어진 문제에 따라 다양한 창 함수를 이용할 수 있다. 기저의 재생성과 interpolation의 수렴성을 소개하고, 수치 예제로서, Poisson 문제를 통해 이 방법의 유효함을 보인다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제1권1호
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• pp.1-34
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• 1997

In this study, various available meshless methods are briefly reviewed and the connection among them is investigated. The objective of meshless methods is to eliminate some difficulties which are originated from reliance on a mesh by constructing the approximation entirely in terms of nodes. Especially, focusing on Element Free Galerkin Method(EFGM) based on moving least square interpolants(MLSI), a new implementation is developed based on a variational principle with penalty function method were used to enforce the essential boundary condition. In addition, the weighted orthogonal basis functions are constructed to overcome disadvantage of MLSI.

• 대한토목학회논문집
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• 제28권6A호
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• pp.835-842
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• 2008

응답면 기법은 수치적 효율성을 증대시키기 위해 구조 신뢰성 해석에 널리 적용되고 있다. 그러나 응답면 기법을 사용한 대형구조물의 신뢰성 해석에는 아직도 과도한 해석시간이 요구되고 비선형성이 큰 한계상태에 대해서는 확률변수에 대한 신뢰도지수의 민감도 측면에서 많은 오차가 발생한다. 그러므로, 이 연구에서는 이동최소제곱근사법을 적용한 새로운 응답면 기법을 제안한다. 기존의 응답면 기법에 사용되어온 최소제곱근사법은 표본점들에 동일한 가중값을 부여하여 응답면 함수의 계수를 결정한다. 반면에 이동최소제곱근사법은 설계점에 가까운 표본점들에 더 높은 가중값을 부여함으로써 설계점 근처에서 한계상태식에 더 가까운 응답면 함수를 제공하여 정확도를 증대시킨다. 이동최소제곱근사법을 이용한 신뢰성 해석 절차를 살펴보면, 먼저 선형 응답면 함수를 생성하여 설계점이 있을 영역을 결정한 다음, 이 영역에서 추출된 표본점들을 이용하여 2차 응답면 함수를 생성한다. 그 다음 단계에서는 기존에 추출된 표본점에 연속적으로 하나의 표본점을 더해가면서 응답면 함수를 더욱더 정확히 근사시킨다. 제안된 방법의 효율성을 검토하기 위해서 기존 연구자에 의해 제안된 수치적 문제 및 트러스 문제들에 대하여 신뢰성 해석을 수행하였다. 그 결과 제안된 방법은 민감도를 포함한 정확성 뿐만 아니라 계산 효율성도 증대시킴을 확인할 수 있었다.

• 한국해양공학회지
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• 제28권2호
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• pp.93-101
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• 2014

In general, particle simulation methods such as the MPS(Moving Particle Simulation) or SPH(Smoothed Particle Hydrodynamics) methods have some serious drawbacks for pressure solutions. The pressure field shows spurious high fluctuations both temporally and spatially. It is well known that pressure fluctuation primarily occurs because of the numerical approximation of the partial differential operators. The MPS and SPH methods employ a pre-defined kernel function in the approximation of the gradient and Laplacian operators. Because this kernel function is constructed artificially, an accurate solution cannot be guaranteed, especially when the distribution of particles is irregular. In this paper, we propose a particle simulation method based on the moving least-square technique for solving the partial differential operators using a Taylor-series expansion. The developed method was applied to the hydro-static pressure and dam-broken problems to validate it.

• 대한기계학회논문집A
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• 제24권10호
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• pp.2469-2476
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• 2000

The meshing of the domain has long been the major bottleneck in performing the finite element analysis. Research efforts which are so-called meshfree methods have recently been directed towards eliminating or at least easing the requirement for meshing of the domain. In this paper, a new meshfree method for solving nonlinear boundary value problem, based on the bubble packing technique and Delaunay triangle is proposed. The method can be efficiently implemented to the problems with singularity by using formly distributed nodes.