• Interaction and multiscale mechanics
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• v.6 no.2
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• pp.173-195
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• 2013

Meshfree methods are known to have the capability to overcome the strict regularization requirements and numerical instabilities that encumber the finite element method (FEM) in large deformation problems. They are also more naturally suited for problems involving material perforation and fragmentation. To take advantage of the high efficiency of FEM and high accuracy of meshfree methods, a coupled finite element (FE) and reproducing kernel (RK, one of the meshfree approximations) formulation is described in this paper. The coupling of FE and RK approximation is implemented in an evolutionary fashion, where the extent and location of the evolution is dependent on a triggering criteria provided by the material constitutive laws. To enhance computational efficiency, Gauss quadrature is applied to integrate both FE and RK domains so that no state variable transfer is required when mesh conversion is performed. To control the hourglassing that might occur with 1-point integrated hexahedral grids, viscous type hourglass control is implemented. Meanwhile, the FEM version of the K&C concrete (KCC) model was modified to make it applicable in both FE and RK formulations. Results using this code and the KCC model are shown for the modeling of concrete responses under quasi-static, blast and impact loadings. These analyses demonstrate that fragmentation phenomena of the sort commonly observed under blast and impact loadings of concrete structures was able to be realistically captured by the coupled formulation.

• Journal of Computing Science and Engineering
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• v.10 no.2
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• pp.58-67
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• 2016

With the large amount of complex network data that is increasingly available on the Web, link prediction has become a popular data-mining research field. The focus of this paper is on a link-prediction task that can be formulated as a binary classification problem in complex networks. To solve this link-prediction problem, a sparse-classification algorithm called "Truncated Kernel Projection Machine" that is based on empirical-feature selection is proposed. The proposed algorithm is a novel way to achieve a realization of sparse empirical-feature-based learning that is different from those of the regularized kernel-projection machines. The algorithm is more appealing than those of the previous outstanding learning machines since it can be computed efficiently, and it is also implemented easily and stably during the link-prediction task. The algorithm is applied here for link-prediction tasks in different complex networks, and an investigation of several classification algorithms was performed for comparison. The experimental results show that the proposed algorithm outperformed the compared algorithms in several key indices with a smaller number of test errors and greater stability.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.773-786
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• 2001

On the setting of the half-space of the Euclidean n-space, we consider harmonic Bergman spaces and we also study properties of the reproducing kernel. Using covering lemma, we find some equivalent quantities. We prove that if lim$ lim\limits_{i\rightarrow\infty}\frac{\mu(K_r(zi))}{V(K_r(Z_i))}$ then the inclusion function $I : b^p\rightarrow L^p(H_n, d\mu)$ is a compact operator. Moreover, we show that if f is a nonnegative continuous function in $L^\infty and lim\limits_{Z\rightarrow\infty}f(z) = 0, then T_f$ is compact if and only if f $\in$ $C_{o}$ (H$_{n}$ ).

• Steel and Composite Structures
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• v.22 no.1
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• pp.161-182
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• 2016

A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) analysis of functionally graded material (FGM) axisymmetric circular plates with simply-supported and clamped edges. The strong formulation of this 3D elasticity axisymmetric problem is derived on the basis of the Reissner mixed variational theorem (RMVT), which consists of the Euler-Lagrange equations of this problem and its associated boundary conditions. The primary field variables are naturally independent of the circumferential coordinate, then interpolated in the radial coordinate using the early proposed DRK interpolation functions, and finally the state space equations of this problem are obtained, which represent a system of ordinary differential equations in the thickness coordinate. The state space DRK solutions can then be obtained by means of the transfer matrix method. The accuracy and convergence of this method are examined by comparing their solutions with the accurate ones available in the literature.

• Interaction and multiscale mechanics
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• v.1 no.3
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• pp.339-355
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• 2008

A Galerkin meshfree method is presented for analyzing shear deformable cylindrical panels. Based upon the analogy between the cylindrical panel and the curved beam a pure bending mode for cylindrical panel is rationally constructed. The meshfree approximation employed herein is characterized by an enhanced moving least square or reproducing kernel basis function that can exactly represent the pure bending mode and thus meets the requirement of Kirchhoff mode reproducing condition. The variational form is discretized using the efficient stabilized conforming nodal integration with a smoothed nodal gradient based curvature. The resulting meshfree formulation satisfies the integration constraint for bending exactness. Moreover, it is shown here that the smoothed gradient preserves several desired properties which are valid for the standard gradient obtained by direct differentiation, such as partition of nullity and reproduction of a constant strain field. The efficacy of the proposed approach is demonstrated by two benchmark cylindrical panel examples.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.450-455
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• 2004

There is few research about contact problem for a rigid surface with an arbitrary shape in SPH. The variational equation based on the virtual work principle is derived and its solution is obtained by the penalty method. It is proposed a new method that can determine the parameters for a penetration and a penetration rate used in the penalty method. The reproducing condition is adopted to correct the deficiency of kernel on the boundary. In order to calculate a penetration of particles, after checking boundary particles for deformable body boundary normal vectors were determined on the rigid surface. Numerical simulations for models which have rigid surface with an arbitrary shape were conducted to validate the proposed method in 2D. The results of those analysis represent that the contact algorithm proposed in this study works properly.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.1 s.232
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• pp.30-37
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• 2005

There is few research about contact problem for a rigid surface with an arbitrary shape in SPH. The variational equation based on the virtual work principle is derived and its solution is obtained by the penalty method. It is proposed a new method that can determine the parameters for a penetration and a penetration rate used in the penalty method. The reproducing condition is adopted to correct the deficiency of kernel on the boundary. In order to calculate a penetration of particles, after checking boundary particles for deformable body, boundary normal vectors were determined on the rigid surface. Numerical simulations for models which have rigid surface with an arbitrary shape were conducted to validate the proposed method in 2D Cartesian and cylindrical coordinate. The results of those analysis represent that the contact algorithm proposed in this study works properly.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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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.

• Journal for History of Mathematics
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• v.15 no.1
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• pp.83-92
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• 2002

Gator Szego was one of the most brilliant Mathematicians. Mathematical science owes him several fundamental contributions in such fields as theory of functions of a complex variables, conformal mapping, Fourier series, theory of orthogonal polynomials, and many others. He wrote the famous Polya-Szego Problems and Theorem in Analysis which is the two volume of concentrated mathematical beauty. In this paper, we mention Szego's life, Szego's work, and Szego reproducing kernel.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.71-84
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• 2017

We discuss the qualitative uncertainty principle for Gabor transform on certain classes of the locally compact groups, like abelian groups, ${\mathbb{R}}^n{\times}K$, K ⋉ ${\mathbb{R}}^n$ where K is compact group. We shall also prove a weaker version of qualitative uncertainty principle for Gabor transform in case of compact groups.