• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.459-474
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• 2018

Cao et al. in (Numer. Linear. Algebra Appl. 18 (2011) 875-895) proposed a splitting method for saddle point problems which unconditionally converges to the solution of the system. It was shown that a Krylov subspace method like GMRES in conjunction with the induced preconditioner is very effective for the saddle point problems. In this paper we first modify the iterative method, discuss its convergence properties and apply the induced preconditioner to the problem. Numerical experiments of the corresponding preconditioner are compared to the primitive one to show the superiority of our method.

• The Pure and Applied Mathematics
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• v.21 no.2
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• pp.129-139
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• 2014

In this paper, we present a detailed comparison of the performance of the numerical solvers such as the biconjugate gradient stabilized, operator splitting, and multigrid methods for solving the two-dimensional Black-Scholes equation. The equation is discretized by the finite difference method. The computational results demonstrate that the operator splitting method is fastest among these solvers with the same level of accuracy.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.3
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• pp.197-207
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• 2013

The Cahn-Hilliard equation was proposed as a phenomenological model for describing the process of phase separation of a binary alloy. The equation has been applied to many physical applications such as amorphological instability caused by elastic non-equilibrium, image inpainting, two- and three-phase fluid flow, phase separation, flow visualization and the formation of the quantum dots. To solve the Cahn-Hillard equation, many numerical methods have been proposed such as the explicit Euler's, the implicit Euler's, the Crank-Nicolson, the semi-implicit Euler's, the linearly stabilized splitting and the non-linearly stabilized splitting schemes. In this paper, we investigate each scheme in finite-difference schemes by comparing their performances, especially stability and efficiency. Except the explicit Euler's method, we use the fast solver which is called a multigrid method. Our numerical investigation shows that the linearly stabilized stabilized splitting scheme is not unconditionally gradient stable in time unlike the known result. And the Crank-Nicolson scheme is accurate but unstable in time, whereas the non-linearly stabilized splitting scheme has advantage over other schemes on the time step restriction.

• Explosives and Blasting
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• v.27 no.2
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• pp.1-11
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• 2009

Abstract By investigating the stress redistribution caused by the preceding cut blasting when applying the pre-splitting method to tunnel round, an attempt was made to find conditions that were favorable for the propagation of cracks in contour holes. The investigation of the direction of minor principal stress in the numerical analysis revealed that the most significant factor affecting the change of the direction was the loading condition, while the core shape, rock type, and tunnel depth seemed to be less important in determining the direction of minor principal stress. Moreover, the number of cracks tended to increase with the increase of deviatoric stress. Through the model test of pre-splitting, it is confirmed that the pre-splitting method taking the stress field into account can reduce the extent of yield zone and has advantage in controlling the direction of crack than the conventional one.

• Tunnel and Underground Space
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• v.31 no.6
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• pp.415-427
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• 2021

This technical report briefly introduced the rock cutting splitting method under development. This method is a method of excavating the rock by splitting the block after the rock cutting process. After designing the cutting geometry of the rock face, the chisel is press-fitted to remove the rock block. At this time, when the cutting block is properly designed, the tensile crack propagates smoothly at the bottom of the rock block. An analytical solution was devised to estimate the indentation force required for splitting rock blocks using fracture toughness mode 1 required for tensile crack growth. The impact force of the hydraulic breaker of the excavator was analyzed, and the grade of the excavator that can be constructed according to the rock block design geometry was analyzed.

• Geomechanics and Engineering
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• v.14 no.3
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• pp.225-231
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• 2018

In this paper, in order to explain the splitting of cylindrical rock specimen under uniaxial loading, cracks in cylindrical rock specimen are divided into two kinds, the longitudinal crack and the slanting crack. Mechanical behavior of the rock is described by elastic-brittle-plastic model and splitting is assumed to suddenly occur when the uniaxial compressive strength is reached. Expression of the stresses induced by the longitudinal crack in direction perpendicular to the major axis of the crack is deduced by using the Maxwell model. Results show that the induced stress is tensile and can be greater than the tensile strength even before the uniaxial compressive strength is reached. By using the Inglis's formula and simplifying the cracks as slender ellipse, the above conclusions that drawn by using the Maxwell model are confirmed. Compared to shearing fracture, energy consumption of splitting seems to be less, and splitting is most likely to occur when the uniaxial loading is great and quick. Besides, explaining the rock core disking occurred under the fast axial unloading by using the Maxwell model may be helpful for understanding that rock core disking is fundamentally a tensile failure phenomenon.

• Proceedings of the Korea Contents Association Conference
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• 2006.11a
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• pp.565-569
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• 2006

This paper reviews some loop partitioning techniques such as loop splitting method by thresholds and Polychronopoulos' loop splitting method for exploiting parallelism from single loop which already developed. We propose improved loop splitting method for maximizing parallelism of single loops with non-constant dependence distances. By using the distance for the source of the first dependence, and by our defined theorems, we present generalized and optimal algorithms for single loops with non-uniform dependences. The algorithms generalize how to transform general single loops into parallel loops.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.3
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• pp.653-661
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• 1994

In this paper the CSCM type upwind flux difference splitting Navier-Stokes method has been applied to study the ARL-SL19 supersonic/transonic compressor cascade flow. H-type grid was chosen for its simplicity in applying cyclic tridiagonal matrix algorithm along with conventional slip/no-slip boundary conditions. The thin-layer algebraic model of Baldwin-Lomax was employed for the calculation of turbulent flows. The test case inlet Mach No. was 1.612 and inlet/exit pressure ratio($P_2/P_1$) was 2.15. The results were compared with experimental results from current method were compared well in suction surface with the experiments and other computational results; however, not well in pressure surface. It might be due to the complex flowfields such as shock/boundary layer interaction, turbulence, and flow separation, etc. In the future, a proper turbulence modelling and adaptive grid system will be studied to improve the solution quality.

• Magazine of the Korea Concrete Institute
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• v.2 no.3
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• pp.89-95
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• 1990

Possibility for the evaluation of fracture properties of mortar and concrete by splitting tensile test was stud¬ied. Splitting tensile tests were conducted to obtain the fracture loads for several sizes of cylindrical specimens of mortar and concrete with initial notch. From the results, fracture energy and fracture toughness by SEL were obtained and compared with the values by Rooke and Cartwright, and r.E.Moo The values by SEL method converged effectively. SEL method was shown to be a good method to obtain fracture properties of mortar and concrete.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.1
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• pp.105-111
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• 1990

In this paper, fast algorithms to generate the codebook of vector quantization in image coding, are proposed. And an efficient algorithm to guess a initial codebook, namely, binary splitting method, is proposed. We generated the initial codebook by binary splitting method and then reduced the searching time using Iterative Optimization algorithm as an alternate to the generalized Lloyd algorithm and several information from binary splitting method. And the searching time and performance can be traded off by varying the searching range. With this proposed algorithm, the computation time can be reduced by a factor of 60 Without any degradation of image quality.