• Nuclear Engineering and Technology
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• v.51 no.1
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• pp.13-30
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• 2019

This paper presents the recent improvements in the DeCART code for HTGR analysis. A new 190-group DeCART cross-section library based on ENDF/B-VII.0 was generated using the KAERI library processing system for HTGR. Two methods for the eigen-mode adjoint flux calculation were implemented. An azimuthal angle discretization method based on the Gaussian quadrature was implemented to reduce the error from the azimuthal angle discretization. A two-level parallelization using MPI and OpenMP was adopted for massive parallel computations. A quadratic depletion solver was implemented to reduce the error involved in the Gd depletion. A module to generate equivalent group constants was implemented for the nodal codes. The capabilities of the DeCART code were improved for geometry handling including an approximate treatment of a cylindrical outer boundary, an explicit border model, the R-G-B checker-board model, and a super-cell model for a hexagonal geometry. The newly improved and implemented functionalities were verified against various numerical benchmarks such as OECD/MHTGR-350 benchmark phase III problems, two-dimensional high temperature gas cooled reactor benchmark problems derived from the MHTGR-350 reference design, and numerical benchmark problems based on the compact nuclear power source experiment by comparing the DeCART solutions with the Monte-Carlo reference solutions obtained using the McCARD code.

• Nuclear Engineering and Technology
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• v.55 no.6
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• pp.2172-2194
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• 2023

A variational nodal method (VNM) with unstructured-mesh is presented for solving steady-state and dynamic neutron diffusion equations. Orthogonal polynomials are employed for spatial discretization, and the stiffness confinement method (SCM) is implemented for temporal discretization. Coordinate transformation relations are derived to map unstructured triangular nodes to a standard node. Methods for constructing triangular prism space trial functions and identifying unique nodes are elaborated. Additionally, the partitioned matrix (PM) and generalized partitioned matrix (GPM) methods are proposed to accelerate the within-group and power iterations. Neutron diffusion problems with different fuel assembly geometries validate the method. With less than 5 pcm eigenvalue (k_eff) error and 1% relative power error, the accuracy is comparable to reference methods. In addition, a test case based on the kilowatt heat pipe reactor, KRUSTY, is created, simulated, and evaluated to illustrate the method's precision and geometrical flexibility. The Dodds problem with a step transient perturbation proves that the SCM allows for sufficiently accurate power predictions even with a large time-step of approximately 0.1 s. In addition, combining the PM and GPM results in a speedup ratio of 2-3.

• Nuclear Engineering and Technology
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• v.54 no.4
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• pp.1195-1205
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• 2022

Recent developments on spectral diffusion algorithms, i.e., algorithms which exploit the projection of the solution on the eigenfunctions of the Laplacian operator, demonstrated their effective applicability in fast transient conditions. Nevertheless, the numerical error introduced by these algorithms, together with the uncertainties associated with model parameters, may impact the reliability of the predictions on short-lived volatile fission product release from nuclear fuel. In this work, we provide an upper bound on the numerical error introduced by the presented spectral diffusion algorithm, in both constant and time-varying conditions, depending on the number of modes and on the time discretization. The definition of this upper bound allows introducing a methodology to a priori bound the numerical error on short-lived volatile fission product retention.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.185-201
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• 2014

In this paper, we construct a numerical method to solve singularly perturbed one-dimensional parabolic convection-diffusion problems. We use Euler method with uniform step size for temporal discretization and exponential-spline scheme on spatial uniform mesh of Shishkin type for full discretization. We show that the resulting method is uniformly convergent with respect to diffusion parameter. An extensive amount of analysis has been carried out to prove the uniform convergence with respect to the singular perturbation parameter. The obtained numerical results show that the method is efficient, stable and reliable for solving convection-diffusion problem accurately even involving diffusion parameter.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.34D no.8
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• pp.41-51
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• 1997

The device simulator (BANDIS) which can analyze efficiently the electrical characteristics of the semiconductor devices under the three dimensional stationary conditions on the IBM PC was developed. Poisson, electon and hole continuity equations are discretized y te galerkin method using a tetrahedron as af finite element. The frontal solver which has exquisite data structures and advanced input/output functions is dused for the matrix solver which needs the highest cost in the three dimensional device simulation. The discretization method of the continuity equations used in BANDIS are compared with that of the scharfetter-gummel method used in the commercial three-dimensional device. To verify an accuracy and the efficiency of the discretization method, the simulation results of the PN junction diode and the BJT from BANDIS are compared with those of the commercial three-dimensiional device simulator such as DAVINCI. The maximum relative error within 2% and the average number of iterations needed for the convergence is decreased by more than 20%. The total simulation time of the BJT with 25542 nodes is decreased to about 60% compared with that of DAVINCI.

• Proceedings of the KIEE Conference
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• 1990.11a
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• pp.413-416
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• 1990

This paper proposes a design procedure based on the LQG/LTR method for a launch vehicle autopilot. Continuous-discrete type LQG/LTR compensators are designed using the $\delta$-transformation [1] in order to overcome numerical problems occurring in the process of discretization. The $\delta$-LQG/LTR compensator using the $\delta$-transformation is compared with the $\delta$-LQG/LTR compensator using the $\delta$-transformation. The performance of the overall system controlled by the $\delta$-LQG/LTR compensator is evaluated via simulations, which show that the discretization error problem is resolved and the control performances are satisfied in the proposed compensator.

• The Journal of the Acoustical Society of Korea
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• v.19 no.2E
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• pp.14-19
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• 2000

The forward propagated ultrasonic fields resulting from a circular plane or a concave transducer in layered fluid media as well as in homogeneous water are theoretically estimated by the angular spectrum method(ASMJ) combined with Rayleigh-Sommerfeld diffraction theory(RSDT), and measured by a precision 3-D scanning system with a needle-point hydrophone. To make the aliasing error negligible on the 2-D FFT in the theoretical estimation, the spatial discretization in the ASM are carefully considered for optimal selection of spatial sampling intervals and the size of discretization area. It is shown that the estimated fields agree reasonably with the measured ones.

• JSTS:Journal of Semiconductor Technology and Science
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• v.4 no.1
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• pp.32-40
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• 2004

An extension of the density-gradient model to include the non-local transport effect is presented. The governing equations can be derived from the first three moments of the Wigner distribution function with some approximations. A new nonlinear discretization scheme is applied to the model to reduce the discretization error. We also developed a new boundary condition for the $Si/SiO_2$ interface that includes the electron wavefunction penetration into the oxide to obtain more accurate C-V characteristics. We report the simulation results of a 25-nm metal-oxide-semiconductor field-effect transistor (MOSFET) device.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.717-737
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• 2014

We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise linear finite element methods for parabolic interface problems. Optimal $L^2(L^2)$ and $L^2(H^1)$ error estimates are shown to hold for semidiscrete problem under suitable regularity of the true solution in whole domain. Further, fully discrete scheme based on backward Euler method has also analyzed and optimal $L^2(L^2)$ norm error estimate is established. The error estimates are obtained for fitted finite element discretization based on straight interface triangles.

• Computational Structural Engineering
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• v.3 no.3
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• pp.125-131
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• 1990

A finite element technique for the time dependent large structural problems is presented. It is based on the error estimation for the bases of solution spaces. An a-posteriori energy norm of residual error serves as the error indicator. Mode shapes which are calculated by scaling the Ritz vectors are applied to discretize the continuous spatial domain. Finally, the performance of the proposed methods is demonstrated by solving simple examples.