• 한국전산유체공학회:학술대회논문집
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• 2008.03a
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• pp.33-41
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• 2008

This paper is an extension of previous study[9] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite serendipity cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires at each element corners four degrees-of-freedom such as the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational bases from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[7].

• 한국전산유체공학회:학술대회논문집
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• 2008.10a
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• pp.33-41
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• 2008

This paper is an extension of previous study[9] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite serendipity cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires at each element corners four degrees-of-freedom such as the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational bases from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[7].

• Journal of the Korean Society for Precision Engineering
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• v.24 no.11
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• pp.144-153
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• 2007

In order to generate the input data for rapid prototyping, a new approach which is based on the implicit surface interpolation method is presented. In the method a surface is reconstructed by creating smooth implicit surface from unorganized cloud of points through which the surface should pass. In the method an implicit surface is defined by the adaptive local shape functions including quadratic polynomial function, cubic polynomial function and RBF(Radial Basis Function). By the reconstruction of a surface, various types of error in raw STL file including degenerated triangles, undesirable holes with complex shapes and overlaps between triangles can be eliminated automatically. In order to get the slicing data for rapid prototyping an efficient intersection algorithm between implicit surface and plane is developed. For the direct usage for rapid prototyping, a robust transformation algorithm for the generation of complete STL data of solid type is also suggested.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.15-15
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• 2000

In the past couple of years, there has been increasing interest in the fusion of neural networks and fuzzy logic. Most of the existing fused models have been proposed to implement different types of fuzzy reasoning mechanisms and inevitably they suffer from the dimensionality problem when dealing with complex real-world problem. To overcome the problem, we propose the self-organizing networks with activation nodes based on fuzzy inference and polynomial function. The proposed model consists of two parts, one is fuzzy nodes which each node is operated as a small fuzzy system with fuzzy implication rules, and its fuzzy system operates with Gaussian or triangular MF in Premise part and constant or regression polynomials in consequence part. the other is polynomial nodes which several types of high-order polynomials such as linear, quadratic, and cubic form are used and are connected as various kinds of multi-variable inputs. To demonstrate the effectiveness of the proposed method, time series data for gas furnace process has been applied.

• Structural Engineering and Mechanics
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• v.21 no.3
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• pp.315-332
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• 2005

The Element-free Galerkin Method has become a very popular tool for the simulation of mechanical problems with moving boundaries. The internally applied Moving Least Squares interpolation uses in general Gaussian or cubic weighting functions and has compact support. Due to the approximative character of this interpolation the obtained shape functions do not fulfill the interpolation conditions, which causes additional numerical effort for the application of the boundary conditions. In this paper a new weighting function is presented, which was designed for meshless shape functions to fulfill these essential conditions with very high accuracy without any additional effort. Furthermore this interpolation gives much more stable results for varying size of the influence radius and for strongly distorted nodal arrangements than existing weighting function types.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.1
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• pp.13-17
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• 2003

A continuous solution of the Dirichlet boundary value problem for the heat equation $u_t$＝$a2u_{xx}$ using a fuzzy system is described. We first apply the Crank-Nicolson method to obtain a discrete solution at the grid points for the heat equation. Then we find a continuous function to represent approximately the discrete values at the grid points in the form of a bicubic spline function (equation omitted) that can in turn be represented exactly by a fuzzy system. We show that the computed values at non-grid points using the bicubic spline function is much smaller than the ones obtained by linear interpolations of the values at the grid points. We also show that the fuzzy rule table in the fuzzy system representation of the bicubic spline function can be viewed as a gray scale image. Hence, the fuzzy rules provide a visual representation of the functions of two variables where the contours of different levels for the function are shown in different gray scale levels

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.477-482
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• 2012

In this note, we investigate partition congruences for a certain type of partition function, which is named as the overcubic partition pairs in light of the literature. Let $\bar{cp}(n)$ be the number of overcubic partition pairs. Then we will prove the following congruences: $$\bar{cp}(8n+7){\equiv}0(mod\;64)\;and\;\bar{cp}(9m+3){\equiv}0(mod\;3)$$.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.19-20
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• 2003

Brownian-dynamics simulation on highly charged colloidal suspensions is performed by employing Tokuyama effective force recently proposed. The radial distribution function suggests that there exist three novel phases, a gas phase, a liquid droplet phase, and a face-centered cubic (FCC) crystal droplet phase, depending on the minimum values of that potential. The dynamics of droplet growth is also investigated both in liquid droplet phase and in crystal droplet phase. Thus, different types of characteristic growth stages are found.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.19-26
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• 1998

The isoparametric spline finite strip method for degenerated shells is presented. In the formulation, both the geometry and the displacement field are represented by uniform cubic B-spline curves. Spline shell strip is degenerated stress-resultant shell with 6 dof at each node;and the penalty function method is used to incorporated the six dof,

• Journal of Korea Foundry Society
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• v.5 no.2
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• pp.125-136
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• 1985

The most desirable method for the solution of solidification problems in castings must be the one which combines accuracy, simplicity, and low computer usage cost. The purpose of the present study is to develop a method which includes all these advantages. The purpose of the present research was approached by the introduction of two methods: (1) A pour-out test, employed with very high purity aluminum, for the purpose of obtaining accurate solidification data in L-sections; and (2) an numerical technique, using the cubic spline function for defining solidification curves.