• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.147-159
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• 1997

It is important to solve the large sparse linear system appeared in many application field such as $AA^Ty={\beta}$ efficiently. In solving this linear system, the sparse solver using the splitting method for the relatively dense column is experimentally better than the direct solver using the Cholesky method.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.727-741
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• 2010

In this paper, we study the convergence of relaxed two-stage multisplitting method using H-compatible splittings or SOR multisplitting as inner splittings and an outer splitting for solving a linear system whose coefficient matrix is an H-matrix. We also provide numerical experiments for the convergence of the relaxed two-stage multisplitting method.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.489-500
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• 2009

In this paper, we study the convergence of relaxed two-stage multisplitting method using M-splittings or SOR multi splitting as inner splittings and an outer splitting for solving a linear system whose coefficient matrix is an M-matrix. We also provide numerical experiments for the convergence of the relaxed two-stage multisplitting method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.5
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• pp.807-814
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• 2003

3D printers are widely used to verify the designs in the early stage of product development, and are required to have short build time. However, the build time is still too long for a quick design review for engineers. This research focuses on how to split the prototype in order to reduce the build time and improve surface roughness. In order to verify the feasibility of prototype splitting, the build time and the roughness have been experimentally measured for various parts and build orientations. Based on the experimental results an expert system was developed for splitting the original CAD mod el by using an efficient splitting method. It can recommend a splitting plane based on build time, surface roughness and the number of divided parts. It is shown that the model splitting reduces the build time significantly and improves surface quality wit bout rough surfaces where the support was removed.

• Journal of Electrical Engineering and Technology
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• v.11 no.1
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• pp.76-85
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• 2016

This paper presents a method of decision on where bus splitting is needed to reduce fault current level of power systems and to satisfy the fault current constraints. The method employs a modified fault current constrained optimal power flow (FCC-OPF) with X variables for the candidate locations of splitting and for decision making on whether to split or not, it adopts soft-discretization by augmenting inversed U-shaped penalty terms. Also, this paper discusses the procedure on the adequate selection of bus splitting locations based on the results of the modified FCC-OPF, to reduce the total number of the actions taken.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.265-276
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• 2019

For a simple implementation, a linear convex splitting scheme was coupled with the Fourier spectral method for the Cahn-Hilliard equation with a logarithmic free energy. However, an inappropriate value of the splitting parameter of the linear scheme may lead to incorrect morphologies in the phase separation process. In order to overcome this problem, we present a nonlinear convex splitting Fourier spectral scheme for the Cahn-Hilliard equation with a logarithmic free energy, which is an appropriate extension of Eyre's idea of convex-concave decomposition of the energy functional. Using the nonlinear scheme, we derive a useful formula for the relation between the gradient energy coefficient and the thickness of the interfacial layer. And we present numerical simulations showing the different evolution of the solution using the linear and nonlinear schemes. The numerical results demonstrate that the nonlinear scheme is more accurate than the linear one.

• Proceedings of the Materials Research Society of Korea Conference
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• 2007.11a
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• pp.58.2-58.2
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• 2007

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.1
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• pp.1-18
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• 2019

In contrast to the well-developed convex splitting schemes for gradient flows of two-component system, there were few efforts on applying the convex splitting idea to gradient flows of multi-component system, such as the vector-valued Cahn-Hilliard (vCH) equation. In the case of the vCH equation, one need to consider not only the convex splitting idea but also a specific method to manage the partition of unity constraint to design an unconditionally energy stable scheme. In this paper, we propose a constrained Convex Splitting (cCS) scheme for the vCH equation, which is based on a convex splitting of the energy functional for the vCH equation under the constraint. We show analytically that the cCS scheme is mass conserving and unconditionally uniquely solvable. And it satisfies the constraint at the next time level for any time step thus is unconditionally energy stable. Numerical experiments are presented demonstrating the accuracy, energy stability, and efficiency of the proposed cCS scheme.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.489-506
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• 2020

The spatial fractional diffusion equation can be discretized by employing the implicit finite difference scheme using the shifted Grünwald formula. The discretized linear system is obtained, whose the coefficient matrix has a diagonal-plus-Toeplitz structure. In order to solve the diagonal-plus-Toeplitz linear system, on the basis of circulant and skew-circulant splitting (CSCS splitting), we construct a new and efficient iterative method, called DSCS iterative methods, which have two parameters. Than we prove the convergence of DSCS methods. As a focus, we derive the simple and effective values of two optimal parameters under some restrictions. Some numerical experiments are carried out to illustrate the validity and accuracy of the new methods.

• Computers and Concrete
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• v.33 no.3
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• pp.265-273
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• 2024

Predicting fracture properties requires an understanding of structural failure behaviour in relation to specimen type, dimension, and notch length. Facture properties are evaluated using various testing methods, wedge splitting test being one of them. The wedge splitting test was numerically modelled three dimensionally using the finite element method on self compacting concrete specimens with varied specimen and notch depths in the current work. The load - Crack mouth opening displacement curves and the angle of rotation with respect to notch opening till failure are used to assess the fracture properties. Furthermore, based on the simulation results, failure curve was built to forecast the fracture behaviour of self-compacting concrete. The fracture failure curve revealed that the failure was quasi-brittle in character, conforming to non-linear elastic properties for all specimen depth and notch depth combinations.