• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.509-518
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• 2001

The purpose of this paper is to propose a numerical algorithm for the problem of coefficient identification of the scalar wave equation based on a local observation on the boundary: Determine the unknown coefficient function with the knowledge of simultaneous Dirichlet and Neumann boundary values on a part of boundary. To find the unknown coefficient function, the unknown Neumann boundary value is also identified. We recast our inverse problem to variational problem. The gradient method is applied to find the minimizing functions. We confirm the effectiveness of our algorithm by numerical experiments.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.23-40
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• 1998

Mixed finite element method is developed to approxi-mate the solution of the initial-boundary value problem for a strongly nonlinear second-order hyperbolic equation in divergence form. Exis-tence and uniqueness of the approximation are proved and optimal-order $L\infty$-in-time $L^2$-in-space a priori error estimates are derived for both the scalar and vector functions approximated by the method.

• Nuclear Engineering and Technology
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• v.43 no.3
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• pp.243-256
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• 2011

This paper considers the concept of analog computing based on a cellular neural network (CNN) paradigm to simulate nuclear reactor dynamics using a time-dependent second order form of the neutron transport equation. Instead of solving nuclear reactor dynamic equations numerically, which is time-consuming and suffers from such weaknesses as vulnerability to transient phenomena, accumulation of round-off errors and floating-point overflows, use is made of a new method based on a cellular neural network. The state-of-the-art shows the CNN as being an alternative solution to the conventional numerical computation method. Indeed CNN is an analog computing paradigm that performs ultra-fast calculations and provides accurate results. In this study use is made of the CNN model to simulate the space-time response of scalar flux distribution in steady state and transient conditions. The CNN model also is used to simulate step perturbation in the core. The accuracy and capability of the CNN model are examined in 2D Cartesian geometry for two fixed source problems, a mini-BWR assembly, and a TWIGL Seed/Blanket problem. We also use the CNN model concurrently for a typical small PWR assembly to simulate the effect of temperature feedback, poisons, and control rods on the scalar flux distribution.

• ETRI Journal
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• v.21 no.1
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• pp.28-39
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• 1999

Koblitz has suggested to use "anomalous" elliptic curves defined over ${\mathbb{F}}_2$, which are non-supersingular and allow or efficient multiplication of a point by and integer, For these curves, Meier and Staffelbach gave a method to find a polynomial of the Frobenius map corresponding to a given multiplier. Muller generalized their method to arbitrary non-supersingular elliptic curves defined over a small field of characteristic 2. in this paper, we propose an algorithm to speed up scalar multiplication on an elliptic curve defined over a small field. The proposed algorithm uses the same field. The proposed algorithm uses the same technique as Muller's to get an expansion by the Frobenius map, but its expansion length is half of Muller's due to the reduction step (Algorithm 1). Also, it uses a more efficient algorithm (Algorithm 3) to perform multiplication using the Frobenius expansion. Consequently, the proposed algorithm is two times faster than Muller's. Moreover, it can be applied to an elliptic curve defined over a finite field with odd characteristic and does not require any precomputation or additional memory.

• Computers and Concrete
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• v.27 no.2
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• pp.153-162
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• 2021

This paper aims to simulate the isotropic elastic damage theory of Liu Jun (2012) using the self-programmed UMAT subroutine in the interface of ABAQUS. Liu Jun (2012)'s method based on the mechanic theory can not be used interactively with the currently commonly used finite element software ABAQUS. The advantage of this method in the paper is that it can interact with ABAQUS and provide a constitutive program framework that can be modified according to user need. The model retains the two scalar damage variables and the corresponding two energy dissipation mechanisms and damage criteria for considering the tensile and compressive asymmetry of concrete. Taking C45 concrete as an example, the relevant damage evolution parameters of its tensile and compressive constitutive model are given. The study demonstrates that the uniaxial tensile stress calculated by the subroutine is almost the same as the Chinese Concrete Design Specification (GB50010) before the peak stress, but ends soon after the peak stress. The stress-strain curve of uniaxial compression calculated by the subroutine is in good agreement with the peak stress in Chinese Concrete Design Specification (GB50010), but there is a certain deviation in the descending stage. In addition, this paper uses the newly compiled subroutine to simulate the shear bearing capacity of the shear key in a new structural system, namely the open-web sandwich slab. The results show that the damage constitutive subroutine has certain reliability.

• Economic and Environmental Geology
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• v.29 no.2
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• pp.183-192
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• 1996

Much computing time and large computer memory are needed to solve the wave equation in a large complex subsurface layer using finite difference method. The time and memory can be reduced by decreasing the number of grid per minimun wave length. However, decrease of grid may cause numerical dispersion and poor accuracy. In this study, we present 49 points weighted average method which save the computing time and memory and improve the accuracy. This method applies a new weighted average to the coordinate determined by transforming the coordinate of conventional 5 points finite difference stars to $0^{\circ}$ and $45^{\circ}$, 25 points finite differenc stars to $0^{\circ}$, $26.56^{\circ}$, $45^{\circ}$, $63.44^{\circ}$ and 49 finite difference stars to $0^{\circ}$, $18.43^{\circ}$, $33.69^{\circ}$, $45^{\circ}$, $56.30^{\circ}$, $71.56^{\circ}$. By this method, the grid points per minimum wave length can be reduced to 2.5, the computing time to $(2.5/13)^3$, and the required core memory to $(2.5/13)^4$ computing with the conventional method.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.2
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• pp.69.2-69.2
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• 2019

To construct a coronal force-free magnetic field, we must impose the boundary normal current density (or three components of magnetic field) as well as the boundary normal field at the photosphere as boundary conditions. The only method that is known to implement these boundary conditions exactly is the method devised by Grad and Rubin (1958). However, the Grad-Rubin method and all its variations (including the fluxon method) suffer from convergence problems. The magnetofrictional method and its variations are more robust than the Grad-Rubin method in that they at least produce a certain solution irrespective of whether the global solution is compatible with the imposed boundary conditions. More than often, the influence of the boundary conditions does not reach beyond one or two grid planes next to the boundary. We have found that the 2D solenoidal gauge condition for vector potentials allows us to implement the required boundary conditions easily and effectively. The 2D solenoidal condition is translated into one scalar function. Thus, we need two scalar functions to describe the magnetic field. This description is quite similar to the Chandrasekhar-Kendall representation, but there is a significant difference between them. In the latter, the toroidal field has both Laplacian and divergence terms while in ours, it has only a 2D Laplacian term. The toroidal current density is also expressed by a 2D Laplacian. Thus, the implementation of boundary normal field and current are straightforward and their effect can permeate through the whole computational domain. In this paper, we will give detailed math involved in this formulation and discuss possible lateral and top boundary conditions and their meanings.

• Journal of the Korean Magnetic Resonance Society
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• v.3 no.1
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• pp.36-43
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• 1999

We present a pulse shape tailored for broadband decoupling for a system of spin-1/2's with scalar couplings as well. In crafting the pulse shape Coherent Averaging Theory and Fourier expansion method are used. The Fourier expansion coefficients are optimized numerically by applying the Simulated Annealing Method. The decoupling performance of the shaped pulse thus designed is then compared with the well-known composite pulse sequence, DIPSI-2. It is shown that the shaped pulse performs well even at the conditions where the DIPSI sequence begins to fail.

• Proceedings of the KIEE Conference
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• 1987.07a
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• pp.22-25
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• 1987

New measurement method of coupled transmission line characteristics is described. This method presents precision calculated values of even- and odd-mode impedances and effective dielectric constants of mictostrip parallel coupled lines from the scalar quantities obtained by transmission coefficients at two different resonance frequencies. Measured impedances and effective dielctric constants are good agreement with predicted values.

• Journal of the Korean Mathematical Society
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• v.61 no.4
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• pp.659-681
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• 2024

We propose V-cycle multigrid methods for vector field problems arising from the lowest order hexahedral Nédélec finite element. Since the conventional scalar smoothing techniques do not work well for the problems, a new type of smoothing method is necessary. We introduce new smoothers based on substructuring with nonoverlapping domain decomposition methods. We provide the convergence analysis and numerical experiments that support our theory.