• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.1
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• pp.23-36
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• 2023

The vector wave equation is widely used in electromagnetic wave analysis. This paper solves the vector wave equation using curl-conforming finite elements. The variational problem is established from Riesz functional based on vector wave equation and the unique existence of weak solution is explored. The edge elements are used in computation and the simulation results are compared with those obtained from a commercial simulator, ANSYS HFSS (high-frequency structure simulator).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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• pp.27-41
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• 2014

In this paper, we present an efficient numerical method for multiphase image segmentation using a multiphase-field model. The method combines the vector-valued Allen-Cahn phase-field equation with initial data fitting terms containing prescribed interface width and fidelity constants. An efficient numerical solution is achieved using the recently developed hybrid operator splitting method for the vector-valued Allen-Cahn phase-field equation. We split the modified vector-valued Allen-Cahn equation into a nonlinear equation and a linear diffusion equation with a source term. The linear diffusion equation is discretized using an implicit scheme and the resulting implicit discrete system of equations is solved by a multigrid method. The nonlinear equation is solved semi-analytically using a closed-form solution. And by treating the source term of the linear diffusion equation explicitly, we solve the modified vector-valued Allen-Cahn equation in a decoupled way. By decoupling the governing equation, we can speed up the segmentation process with multiple phases. We perform some characteristic numerical experiments for multiphase image segmentation.

• 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.

• Architectural research
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• v.13 no.1
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• pp.17-24
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• 2011

Isogeometric solution of Poisson equation is provided. NURBS (NonUniform B-spline Surface) is introduced to express both geometry of structure and unknown field of governing equation. The terms of stiffness matrix and load vector are consistently derived with very accurate geometric definition. The validity of the isogeometric formulation is demonstrated by using two numerical examples such as square plate and L-shape plate. From numerical results, the present solutions have a good agreement with analytical and finite element (FE) solutions with the use of a few cells in isogeometric analysis.

• Communications of the Korean Mathematical Society
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• v.26 no.2
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• pp.237-251
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• 2011

In this paper, we determine some stability results concerning the 2-dimensional vector variable quadratic functional equation f(x+y, z+w) + f(x-y, z-w) = 2f(x, z) + 2f(y, w) in intuitionistic fuzzy normed spaces (IFNS). We dene the intuitionistic fuzzy continuity of the 2-dimensional vector variable quadratic mappings and prove that the existence of a solution for any approximately 2-dimensional vector variable quadratic mapping implies the completeness of IFNS.

• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.397-407
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• 2012

Let X and Y be vector spaces. We introduce a new type of a cubic functional equation $f$ : $X{\rightarrow}Y$. Furthermore, we assume X is a vector space and (Y, N) is a fuzzy Banach space and then investigate a fuzzy version of the generalized Hyers-Ulam stability in fuzzy Banach space by using fixed point method for the cubic functional equation.

• Structural Engineering and Mechanics
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• v.4 no.2
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• pp.139-148
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• 1996

Vector algorithms and the relative importance of the four basic modules (computation of element stiffness matrices, assembly of the global stiffness matrix, solution of the system of linear simultaneous equations, and calculation of stresses and strains) of a finite element computer program for inelastic analysis of reinforced concrete shells are presented. Performance of the vector program is compared with a scalar program. For a cooling tower problem, the speedup factor from the scalar to the vector program is 34 for the element stiffness matrices calculation, 25.3 for the assembly of global stiffness matrix, 27.5 for the equation solver, and 37.8 for stresses, strains and nodal forces computations on a Gray Y-MP. The overall speedup factor is 30.9. When the equation solver alone is vectorized, which is computationally the most intensive part of a finite element program, a speedup factor of only 1.9 is achieved. When the rest of the program is also vectorized, a large additional speedup factor of 15.9 is attained. Therefore, it is very important that all the modules in a nonlinear program are vectorized to gain the full potential of the supercomputers. The vector finite element computer program for inelastic analysis of RC shells with layered elements developed in the present study enabled us to perform mesh convergence studies. The vector program can be used for studying the ultimate behavior of RC shells and used as a design tool.

• Progress in Medical Physics
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• v.7 no.1
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• pp.53-64
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• 1996

Purpose: The purposes of this paper are to develop a theoretical basis that the beam directions should be considered when the mechanical accuracy of teletherapy machine is evaluated by the star pattern test, to develop methods using asymmetric field in length to simulate beam direction for the case that beam direction does not appear on film. Method: In evaluating mechanical rotational accuracy of the gantry of teletherapy unit by the star pattern test, the direction of radiation beams was considered. A star pattern using some narrow beams was made. Density profiles at 10cm far from estimated gantry axis on the star pattern were measured using an optical densitometer. On each profile, one coordimate of a beam axis was determined. A pair of coordinates on a beam axis form an equation of the axis. Assume that a unit vector equation omitted is with same direction as radiation beam and a vector equation omitted is a vector directing to the beam axis from the estimated gantry axis. Then, a vector product equation omitted ${\times}$ equation omitted is an area vector of which the absolute value is equal to the distance from the estimated gantry axis to the beam axis. The coordinate of gantry axis was obtained by using least-square method for the area vectors relative to the average of whole area vectors. For the axis, the maximum of absolute value of area vectors would be an accuracy of the gantry rotation axis. For the evaluation of mechanical accuracies of collimator and couch axes for which beam direction could not be depicted on a star pattern test film, narrow beams asymmetric in field length was used to simulate beam direction. Result: For a star test pattern to evaluate the mechanical accuracy of rotational axes of a telectherapy machine, the result considering beam direction was different from that ignoring beam direction. For the evaluation of mechanical accuracies of collimator and couch axes by means of a star pattern test, narrow asymmetric beams could simulate beam direction. Conclusion: When a star pattern test is used to evaluate the mechanical accuracy of a teletherapy unit, beam direction must be considered or simulated, and quantitatively evaluated.

• Journal of Advanced Marine Engineering and Technology
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• v.8 no.1
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• pp.64-71
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• 1984

In this paper, the fundemental equation on the Trans-vector control of 3.phi. Induction motor drive and the new equivalent circuit to be adapted for this equation, have been obtained, and control drives system to be coincide with this equation is made. Therefore, it has been obtained that control scheme can always be used motor drive. 3.phi. Induction motor drive has been got the dynamic behavior the same as that of DC motor drive. The drive dynamic response is very rapid because of Trans-vector control on the I_1$ (primary current) and .${\omega}_1$ (frequency of primary current) of the Induation mechine. This paper indicates that a practicality of the drive control system and the rationalty of the theory have been identified with the experimental results. The effect of parameter variations on the drive dynamic response can be evaluated from these results.

• Proceedings of the KIEE Conference
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• 1991.07a
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• pp.637-640
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• 1991

In this paper deals with linearized control of induction motor by vector control. Output equation induced from d-q axies voltage and current equation of induction moter. The condition of induced equation is that rotor's current of axies has 0 and state current of D axies which was driven by synchronous speed is constant. The fully digital controlled induction motor drive system based on the proposed linearized method and the control circuit of system consists of 16bits micro computer and all the function are implemented with software. When the voltage source inverter control with PI controller is empolyed, in spite of secondary resistance Rr Variation, the Vector control condition is satisfied.