• Korean Journal of Mathematics
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• v.28 no.4
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• pp.865-875
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• 2020

We provide detailed proofs for local gradient estimates for weak solutions to elliptic equations in divergence form with partial Dini mean oscillation coefficients subject to conormal derivative boundary conditions.

• 한국전산유체공학회:학술대회논문집
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• 2008.08a
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• pp.58.1-58.1
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• 2008

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.9
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• pp.1320-1327
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• 2004

An efficient boundary-based technique is developed for addressing shape design sensitivity analysis in supercavitating flow problem. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in potential flow problems. The formula, which is expressed in terms of the boundary solutions and shape variation vectors, can be conveniently used for gradient computation in a variety of shape design in potential flow problems. While the sensitivity can be calculated independent of the analysis means, such as the finite element method (FEM) or the boundary element method (BEM), the FEM is used for the analysis in this study because of its popularity and easy-to-use features. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The supercavitating flow problem is chosen to illustrate the efficiency of the proposed methodology. Implementation issues for the sensitivity analysis and optimization procedure are also addressed in this flow problem.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1047-1052
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• 2004

An efficient boundary-based technique is developed for addressing shape design sensitivity analysis in supercavitating flow problem. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in potential flow problems. The formula, which is expressed in terms of the boundary solutions and shape variation vectors, can be conveniently used for gradient computation in a variety of shape design in potential flow problems. While the sensitivity can be calculated independent of the analysis means, such as the finite element method (FEM) or the boundary element method (BEM), the FEM is used for the analysis in this study because of its popularity and easy-touse features. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The supercavitating flow problem is chosen to illustrate the efficiency of the proposed methodology. Implementation issues for and optimization procedure are addressed in this flow problem.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.3
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• pp.255-263
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• 2005

This paper proposes an efficient boundary-based technique for the shape design sensitivity analysis in various disciplines. An analytical sensitivity formula in the form of a boundary integral is derived based on the continuum formulation for a general functional defined in the problems. The formula can be conveniently used for gradient computation in a variety of shape design problems. The advantage of using a boundary-based method is that the shape variation vectors are needed only on the boundary, not over the whole domain. The boundary shape variation vectors are conveniently computed by using finite. Perturbations of the shape geometry instead of complex analytical differentiation of the geometry functions. The potential flow problems and fillet problem are chosen to illustrate the efficiency of the proposed methodology.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1495-1515
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• 2015

This paper deals with the numerical methods for the reconstruction of the source term in a linear parabolic equation from final overdetermination. We assume that the source term has the form f(x)h(t) and h(t) is given, which guarantees the uniqueness of the inverse problem of determining the source term f(x) from final overdetermination. We present the regularization methods for reconstruction of the source term in the whole real line and with Neumann boundary conditions. Moreover, we show the connection of the solutions between the problem with Neumann boundary conditions and the problem with no boundary conditions (on the whole real line) by using the extension method. Numerical experiments are done for the inverse problem with the boundary conditions.

• Journal of the Korean Society for Precision Engineering
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• v.9 no.2
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• pp.44-51
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• 1992

This paper is concerned with the propram of the automatic mesh generation for 2-dimensional domain which contains the curved boundaries and holes. This program treats a new vertical-line drawing method. This method starts with 4-subdivisions of problem domain and the classification of the cross points of grid lines and boundaries. The new node is generated by the vertical line to the line connecting the two intersections of a boundary and two grid lines in gereral. And the node very close to the boundary is moved to the boundary. The automatic mesh generation composed of only rectangular elements is achieved by this procedure. The boundaries are piecewise-curves composed of lines, circles, arcs, and free curves. The free curves are generated by B-Spline form. Although there were some bad elements for the complex boundary, it was possible to obtain the acceptible rectangular elements for the given boundaries.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.1
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• pp.11-21
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• 2004

In this paper, an active vibration control of a tensioned elastic axially moving string is investigated. The dynamics of the translating string ale described by a non-linear partial differential equation coupled with an ordinary differential equation. The time varying control in the form of the right boundary transverse motions is suggested to stabilize the transverse vibration of the translating continuum. A control law based on Lyapunov's second method is derived. Exponential stability of the translating string under boundary control is verified. The effectiveness of the proposed controller is shown through the simulations.

• The Korean Journal of Ceramics
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• v.4 no.3
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• pp.207-212
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• 1998

By comparison of the experimental results in two systems of ZnO varistors, it's appear that Sb2O3 is the indispensable element for twining in ZnO varistors and the Zn7Sb2O12 spinel acts as the nucleus to form twins. Al2O3 is not the origin of twining in ZnO varistor, but it was found that Al2O3 could strengthen the twining and form a deformation twining by ZnAl2O4 dragging and pinning effect. The inhibition ratios of grain and nonuniformity of two systems ZnO varistors increase with the increase of Al2O3 content. The twins affect the inhibition of grain growth, the mechanism could be explained follow as: twins increase the mobility viscosity of ZrO grain and grain boundary, and drag ZrO grain and liquid grain boundary during the sintering, then the grain growth is inhibited and the microstructure becomes more uniform.

• Coupled systems mechanics
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• v.12 no.4
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• pp.337-364
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• 2023

The Rayleigh wave propagation is considered in the structure of the functionally graded piezoelectric material (FGPM) layer over the elastic substrate. The elastic substrate loosely bonds the layer through a corrugated interface, whereas its upper boundary is also corrugated but stress-free. Additionally, the solutions for the FGPM layer and substrate are derived using the fundamental variable separable approach to convert the partial differential equation to an ordinary differential equation. The results with boundary conditions lead to dispersion relations for the electrically open and electrically short cases in the determinant form. The outcomes have been numerically analyzed using a specific model. The findings were presented in the form of graphs, which were created using Mathematica 7. Graphs are plotted for variations in wavenumber and phase velocity. The outcomes may help measure interface defects and design Surface Acoustic Wave (SAW) devices.