• Nuclear Engineering and Technology
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• 제52권6호
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• pp.1137-1147
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• 2020

The discrete ordinates method (S_N) is one of the major shielding calculation method, which is suitable for solving deep-penetration transport problems. Our objective is to explore the available quadrature sets and to improve the accuracy in shielding problems involving strong anisotropy. The linear discontinuous finite-element (LDFE) quadrature sets based on the icosahedron (in short, ICLDFE quadrature sets) are developed by defining projected points on the surfaces of the icosahedron. Weights are then introduced in the integration of the discontinuous finite-element basis functions in the relevant angular regions. The multivariate secant method is used to optimize the discrete directions and their corresponding weights. The numerical integration of polynomials in the direction cosines and the Kobayashi benchmark are used to analyze and verify the properties of these new quadrature sets. Results show that the ICLDFE quadrature sets can exactly integrate the zero-order and first-order of the spherical harmonic functions over one-twentieth of the spherical surface. As for the Kobayashi benchmark problem, the maximum relative error between the fifth-order ICLDFE quadrature sets and references is only -0.55%. The ICLDFE quadrature sets provide better integration precision of the spherical harmonic functions in local discrete angle domains and higher accuracy for simple shielding problems.

• Nuclear Engineering and Technology
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• 제55권2호
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• pp.769-779
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• 2023

This paper describes an hp-angular adaptivity algorithm in the discrete ordinates method for Boltzmann transport applications with strong angular effects. This adaptivity uses discontinuous finite element quadrature sets with different degrees, which updates both angular mesh and the degree of the underlying discontinuous finite element basis functions, allowing different angular local refinement to be applied in space. The regular and goal-based error metrics are considered in this algorithm to locate some regions to be refined. A mapping algorithm derived by moment conservation is developed to pass the angular solution between spatial regions with different quadrature sets. The proposed method is applied to some test problems that demonstrate the ability of this hp-angular adaptivity to resolve complex fluxes with relatively few angular unknowns. Results illustrate that a reduction to approximately 1/50 in quadrature ordinates for a given accuracy compared with uniform angular discretization. This method therefore offers a highly efficient angular adaptivity for investigating difficult particle transport problems.

• ETRI Journal
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• 제39권4호
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• pp.514-524
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• 2017

In this paper, we propose a spatial modulation (SM) scheme referred to as complex quadrature SM (CQSM). In contrast to quadrature SM (QSM), CQSM transmits two complex signal constellation symbols on the real and quadrature spatial dimensions at each channel use, increasing the spectral efficiency. To achieve that, signal symbols transmitted at any given time instant are drawn from two different modulation sets. The first modulation set is any of the conventional QAM/PSK alphabets, while the second is a rotated version of it. The optimal rotation angle is obtained through simulations for several modulation schemes and analytically proven for the case of QPSK, where both results coincide. Simulation results showed that CQSM outperformed QSM and generalized SM by approximately 5 dB and 4.5 dB, respectively, for the same transmission rate. Its performance was similar to that of QSM; however, it achieved higher transmission rates. It was additionally shown numerically and analytically that CQSM outperformed QSM for a relatively large number of transmit antennas.

• Journal of Electrical Engineering and Technology
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• 제10권3호
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• pp.1188-1200
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• 2015

A unified numerical method for computing the quadrature weights, integration matrix, and differentiation matrix is newly developed in this study. For this purpose, a spline-like interpolation using piecewise continuous polynomials is converted into a global spline interpolation formula, with which the quadrature formulas can be derived from integration and differentiation of the transformed function in an exact manner. To prove the usefulness of the suggested approach, both the Lagrange and tension spline interpolations are represented in exactly the same form as global spline interpolation. The applicability of the proposed method on arbitrary nodes is illustrated using two different sets of nodes. A series of validations using three test functions is conducted to show the flexibility in selecting computational nodes with the present method.

• 에너지공학
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• 제16권1호
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• pp.46-52
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• 2007

특정한 방향에 대해 방향중성자속(angular neutron flux)을 정의하는 방향차분 방정식(discrete-ordinates or $S_{N}$ equation)과 달리 방향변수를 구분된 방향영역에 대하여 적분한 값을 사용하고, 해당 방향영역 내에서 방향중성자속이 일정하다고 가정하는 영역상수법(piecewise-constant method)을 개발하였다. 기존 방향차분법과 본 연구에서 개발된 영역상수법을 1계 수송방정식(1'st-order Boltzmann transport equation)과 2계 우성 방정식(even-parity equation)에 적용하여 방향차분 방정식인 $S_{N}$ 방정식과 유사 방향차분방정식($S_{N}$-like equation)인 $PC_{N}$ 방정식을 유도하였다. 우성 방정식에 영역상수법을 적용한 경우 기존 방향차분법의 단점인 광첨두 현상(ray effect)이 현저히 감소함을 확인하였는데 이는 우성 방정식의 혼합 미분항의 기여도가 작아지기 때문인 것으로 판단된다. 이러한 이론은 우성 방정식에서 혼합 미분항이 제거된 단순우성 방정식(simplified even-parity equation)을 사용하는 경우 광첨두 현상이 완전 제거 또는 극단적으로 감소되었던 이전의 결과를 이론적으로 설명한다.

• Structural Engineering and Mechanics
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• 제22권3호
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• pp.331-349
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• 2006

The stresses and deflections in a laminated rectangular plate under thermal vibration are determined by using the moving least squares differential quadrature (MLSDQ) method based on the first order shear deformation theory. The weighting coefficients used in MLSDQ approximation are obtained through a fast computation of the MLS shape functions and their partial derivatives. By using this method, the governing differential equations are transformed into sets of linear homogeneous algebraic equations in terms of the displacement components at each discrete point. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Solving this set of algebraic equations yields the displacement components. Then substituting these displacements into the constitutive equation, we obtain the stresses. The approximate solutions for stress and deflection of laminated plate with cross layer under thermal load are obtained. Numerical results show that the MLSDQ method provides rapidly convergent and accurate solutions for calculating the stresses and deflections in a multi-layered plate of cross ply laminate subjected to thermal vibration of sinusoidal temperature including shear deformation with a few grid points.

• 한국안전학회지
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• 제12권4호
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• pp.220-229
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• 1997

곡선보(curved beam)의 등분포 하중하에서 평면내(in-plane)와 평면의(out-of-plane)의 좌굴(buckling)을 해석하는데 differential quadrature method (DQM)을 이용하여 다양한 경계조건(boundary conditions)과 굽힘각(opening angles)에 따른 입계하중(critical loads)을 계산하였다. DQM의 해석결과는 해석적 해답(exact solution) 또는 다른 수지해석 결과와 비교하였으며, DQM은 적은 요소(grid points)를 사용하여 정확한 해석결과를 보여주었다. 두 경계조건(고정-고정, 고정-단순지지)하에서 새로운 결과를 또한 제시하였다.

• ETRI Journal
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• 제42권4호
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• pp.562-574
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• 2020

Quadrature spatial modulation (QSM) utilizes the in-phase and quadrature spatial dimensions to transmit the real and imaginary parts of a single signal symbol, respectively. The improved QSM (IQSM) transmits two signal symbols per channel use through a combination of two antennas for each of the real and imaginary parts. The main contributions of this study can be summarized as follows. First, we derive an upper bound for the error performance of the IQSM. We then design constellation sets that minimize the error performance of the IQSM for several system configurations. Second, we propose a double QSM (DQSM) that transmits the real and imaginary parts of two signal symbols through any available transmit antennas. Finally, we propose a parallel IQSM (PIQSM) that splits the antenna set into equal subsets and performs IQSM within each subset using the same two signal symbols. Simulation results demonstrate that the proposed constellations significantly outperform conventional constellations. Additionally, DQSM and PIQSM provide a performance similar to that of IQSM while requiring a smaller number of transmit antennas and outperform IQSM with the same number of transmit antennas.

• International Journal of Internet, Broadcasting and Communication
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• 제11권3호
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• pp.27-33
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• 2019

Quadrature spatial modulation (QSM) utilizes the in-phase and quadrature spatial dimensions to transmit the real and imaginary parts, respectively, of a single signal symbol. Improved QSM (IQSM) builds upon QSM to increase the spectral efficiency by transmitting the real and imaginary parts of two signal symbols using antenna combinations of size of two. In this paper, we propose a double QSM (DQSM) scheme that transmits the real and imaginary parts of two signal symbols independently through any of the transmit antennas. The two signal symbols are drawn from two different constellations of the same size with the first symbol drawn from any of the conventional modulation sets while the second is drawn from an optimally rotated version of the first constellation. The optimum rotation angle is obtained through extensive Monte Carlo simulations to minimize the bit error rate (BER) of the system. Simulation results show that for a given spectral efficiency, DQSM performsrelatively close to IQSM while requiring a smaller number of transmit antennas, and outperformsIQSM by up to 2 dB when the same number of antennas are used.

• Nuclear Engineering and Technology
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• 제54권7호
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• pp.2625-2634
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• 2022

Discretization errors are extremely challenging conundrums of discrete ordinates calculations for radiation transport problems with void regions. In previous work, we have presented a multi-collision source method (MCS) to overcome discretization errors, but the efficiency needs to be improved. This paper proposes a goal-oriented algorithm for the MCS method to adaptively determine the partitioning of the geometry and dynamically change the angular quadrature in remaining iterations. The importance factor based on the adjoint transport calculation obtains the response function to get a problem-dependent, goal-oriented spatial decomposition. The difference in the scalar fluxes from one high-order quadrature set to a lower one provides the error estimation as a driving force behind the dynamic quadrature. The goal-oriented algorithm allows optimizing by using ray-tracing technology or high-order quadrature sets in the first few iterations and arranging the integration order of the remaining iterations from high to low. The algorithm has been implemented in the 3D transport code ARES and was tested on the Kobayashi benchmarks. The numerical results show a reduction in computation time on these problems for the same desired level of accuracy as compared to the standard ARES code, and it has clear advantages over the traditional MCS method in solving radiation transport problems with reflective boundary conditions.