• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.4
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• pp.223-231
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• 2019

A continuum-based design sensitivity analysis(DSA) method is developed for electrostatic problems. To consider high order objective functions, we use 9-node finite element basis functions for analysis and DSA methods. As the design variables are parameterized with B-spline functions, smooth boundary variations are naturally obtained. To solve mesh entanglement problems during the optimization process, a mesh regularization scheme is employed. By minimizing the Dirichlet energy functional, mesh uniformity can be automatically achieved. In numerical examples for maximizing dielectrophoresis forces, the numerical results are compared with well-known electrode geometries and the obtained characteristics are discussed.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.6
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• pp.307-317
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• 2002

In this paper we propose a new mesh reconstruction scheme that produces a displaced subdivision surface directly from unorganized points. The displaced subdivision surface is a new mesh representation that defines a detailed mesh with a displacement map over a smooth domain surface, but original displaced subdivision surface algorithm needs an explicit polygonal mesh since it is not a mesh reconstruction algorithm but a mesh conversion (remeshing) algorithm. The main idea of our approach is that we sample surface detail from unorganized points without any topological information. For this, we predict a virtual triangular face from unorganized points for each sampling ray from a parameteric domain surface. Direct displaced subdivision surface reconstruction from unorganized points has much importance since the output of this algorithm has several important properties: It has compact mesh representation since most vertices can be represented by only a scalar value. Underlying structure of it is piecewise regular so it ran be easily transformed into a multiresolution mesh. Smoothness after mesh deformation is automatically preserved. We avoid time-consuming global energy optimization by employing the input data dependant mesh smoothing, so we can get a good quality displaced subdivision surface quickly.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.139-148
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• 2006

Catmull-Clark subdivision scheme provides a powerful method for building smooth and complex surfaces. But the number of faces in the uniformly refined meshes increases exponentially with respect to subdivision depth. Adaptive tessellation reduces the number of faces needed to yield a smooth approximation to the limit surface and, consequently, makes the rendering process more efficient. In this paper, we present a new adaptive tessellation method for general Catmull-Clark subdivision surfaces. Different from previous control mesh refinement based approaches, which generate approximate meshes that usually do not interpolate the limit surface, the new method is based on direct evaluation of the limit surface to generate an inscribed polyhedron of the limit surface. With explicit evaluation of general Catmull-Clark subdivision surfaces becoming available, the new adaptive tessellation method can precisely measure error for every point of the limit surface. Hence, it has complete control of the accuracy of the tessellation result. Cracks are avoided by using a recursive color marking process to ensure that adjacent patches or subpatches use the same limit surface points in the construction of the shared boundary. The new method performs limit surface evaluation only at points that are needed for the final rendering process. Therefore it is very fast and memory efficient. The new method is presented for the general Catmull-Clark subdivision scheme. But it can be used for any subdivision scheme that has an explicit evaluation method for its limit surface.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.5_6
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• pp.288-296
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• 2004

This paper proposes a new mesh simplification algorithm using differential error metric. Many simplification algorithms make use of a distance error metric, but it is hard to measure an accurate geometric error for the high-curvature region even though it has a small distance error measured in distance error metric. This paper proposes a new differential error metric that results in unifying a distance metric and its first and second order differentials, which become tangent vector and curvature metric. Since discrete surfaces may be considered as piecewise linear approximation of unknown smooth surfaces, theses differentials can be estimated and we can construct new concept of differential error metric for discrete surfaces with them. For our simplification algorithm based on iterative edge collapses, this differential error metric can assign the new vertex position maintaining the geometry of an original appearance. In this paper, we clearly show that our simplified results have better quality and smaller geometry error than others.

• Korean Journal of Computational Design and Engineering
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• v.9 no.2
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• pp.143-147
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• 2004

To design parts satisfying physical property in the continuous region, we do it in the discrete rectangular mesh points. Then we obtain points data from parts design and usually construct the surface using least squares method. In such case, that surface has an oscillation in the ineffective region which is inadequate for physical phenomena or NC machining. To solve both problems simultaneously, we extend the surface smoothly to have small curvature in the extended region. Up to now, we use the least squares method for the parts design in Color Picture Tube or Color Display Tube but in this paper, we use functions which is easily controllable. This surface has no error within the effective region compared to the least squares method.

• Transactions of the Korean Society of Automotive Engineers
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• v.11 no.6
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• pp.164-170
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• 2003

The finite element analysis of tires has been conventionally performed by either neglecting tread pattern or modeling only circumferential grooves. Besides, the tire analysis has been mainly limited to static or steady state rolling analysis. In this paper, a transient dynamic analysis of a patterned tire rolling over a cleat with an explicit finite element program is presented. The patterned tire with detailed tread blocks is modeled by a systematic mesh generation procedure, in which tire body and tread pattern meshes are separately generated in the beginning and then both meshes are combined by the tie constraint method. The cleat impact analysis is conducted by using both the patterned tire and the smooth tire models to predict the cleat enveloping characteristics. It is seen that the analysis results of the patterned tire model are in a good agreement with the experimental results.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.4
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• pp.58-67
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• 1998

A sectional analysis of sheet metal forming process with an arbitrary tool shape is proposed in the present work. To improve the numerical convergence in the conventional membrane sectional analysis, the Bending Energy Augmented Membrane (BEAM) elements had been developed. The BEAM elements particularly improve the stability and convergence of the finite element method for the case of deep drawing. In this work, the FERGUBON spline (C$^2$-continuous) was used to fit the deformed mesh to smooth the given curves and calculate the local curvature of the deformed sheet. The fittings of the deformed sheet and tool surface profile ensure the stability and the convergence of the finite element analysis of highly nonlinear stamping processes. A center floor section and front fender section are analyzed to show the accuracy and robustness of the approach. The results obtained by the proposed approach are compared with the available experimental data.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.167.6-167
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• 2001

The cylindrical environment maps of image-based representation methods make high-quality, simple and low-price real-time navigation possible. In this paper, we propose a method to navigate from one viewpoint to the next in the virtual inside space, composed of several cylindrical environment maps. Our system is classified into the two modules. first of all, the panoramic image viewer that employs the rotation and zoom-in/out methods to navigate the virtual inside space, such as the Quicklime VR. The other is smooth real-time navigation using cubic mesh interpolation when the viewpoint moves from one environment map to another in the virtual space.

• 한국전산유체공학회:학술대회논문집
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• 1999.11a
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• pp.95-107
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• 1999

The spatial error due to the non-conservative interpolation become first-order when second-order conservative schemes are used, discontinuities are located away from the overlapped regions, and if the length of the overlapped region is not proportional to the grid spacing. Therefore, the solution accuracy is ensured if two domains overlap each other with a fixed grid point and the interpolation is occurred in smooth flow regions. To validate the spatial and temporal accuracy due to the non-conservative interpolation, inviscid and viscous problems are tested.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.3
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• pp.211-236
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• 2019

This paper is devoted to the study and investigation of the Runge-Kutta discontinuous Galerkin method for a system of differential equations consisting of two hyperbolic conservation laws. The numerical coupling flux which is used at a given interface (x = 0) is the upwind flux. Moreover, in the linear case, we derive optimal convergence rates in the $L_2$-norm, showing an error estimate of order ${\mathcal{O}}(h^{k+1})$ in domains where the exact solution is smooth; here h is the mesh width and k is the degree of the (orthogonal Legendre) polynomial functions spanning the finite element subspace. The underlying temporal discretization scheme in time is the third-order total variation diminishing Runge-Kutta scheme. We justify the advantages of the Runge-Kutta discontinuous Galerkin method in a series of numerical examples.