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Статті в журналах з теми "Method analysis grids"

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Автор: Grafiati

Опубліковано: 4 травня 2024

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1

Xu, Dan, Xiaogang Deng, Yaming Chen, Guangxue Wang, and Yidao Dong. "Effect of Nonuniform Grids on High-Order Finite Difference Method." Advances in Applied Mathematics and Mechanics 9, no. 4 (January 18, 2017): 1012–34. http://dx.doi.org/10.4208/aamm.2016.m1477.

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AbstractThe finite difference (FD) method is popular in the computational fluid dynamics and widely used in various flow simulations. Most of the FD schemes are developed on the uniform Cartesian grids; however, the use of nonuniform or curvilinear grids is inevitable for adapting to the complex configurations and the coordinate transformation is usually adopted. Therefore the question that whether the characteristics of the numerical schemes evaluated on the uniform grids can be preserved on the nonuniform grids arises, which is seldom discussed. Based on the one-dimensional wave equation, this paper systematically studies the characteristics of the high-order FD schemes on nonuniform grids, including the order of accuracy, resolution characteristics and the numerical stability. Especially, the Fourier analysis involving the metrics is presented for the first time and the relation between the resolution of numerical schemes and the stretching ratio of grids is discussed. Analysis shows that for smooth varying grids, these characteristics can be generally preserved after the coordinate transformation. Numerical tests also validate our conclusions.

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2

Tang, Bi Qiang, Yi Jun Yu, Shu Hai Feng, and Feng Li. "A Novel Method of Static Security Analysis Based on Multithread Technology." Advanced Materials Research 732-733 (August 2013): 639–45. http://dx.doi.org/10.4028/www.scientific.net/amr.732-733.639.

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With the UHV (Ultra High Voltage) power grid construction and the interconnection of regional power grids, the scale of power grids in China is increasing rapidly. At the same time, significant uncertainty and variability is being introduced into power grid operation with the integration of large-scale renewable energy in power systems. All of these pose an enormous challenge to the operation control of power systems in China. For a long time, online static security analysis, as an important part of EMS (Energy Management System), has been an effective tool for power grid operation. However, it is increasingly difficult for traditional static security analysis in serial computing mode to be online applied in bulk power grids in China. A new practical parallel approach for online static security analysis is put forward in this paper. A multithread parallelism is introduced into contingency screening, detailed contingency evaluation and decision support for reducing the execution time. By employing the multithread technology, the hardware resources of multi-processor/multi-core computer can be fully used and the program can be speeded up effectively. The performance of the parallel static security analysis is demonstrated by tests on two large-scale power systems. The test results show that the proposed method can be online applied in real bulk power grids.

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3

Chan, H. C., C. W. Cai, and Y. K. Cheung. "An Analytical Method for Static Analysis of Double Layer Grids." International Journal of Space Structures 4, no. 2 (June 1989): 107–16. http://dx.doi.org/10.1177/026635118900400204.

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An analytical method for the static analysis of double layer grids consisting of diagonals and top and bottom layers which are plane orthogonal grids is presented. It is assumed that the double layer grid is simply supported at all nodes located at the boundary of the top layer. By using the double U-transformation technique, exact solutions for the nodal displacements and axial forces of the bars in the double layer grid can be derived. The validity of the method is demonstrated with a simple example.

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4

Hansbo, Anita, Peter Hansbo, and Mats G. Larson. "A finite element method on composite grids based on Nitsche's method." ESAIM: Mathematical Modelling and Numerical Analysis 37, no. 3 (May 2003): 495–514. http://dx.doi.org/10.1051/m2an:2003039.

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5

Martynenko, S. I. "Potentialities of the Robust Multigrid Technique." Computational Methods in Applied Mathematics 10, no. 1 (2010): 87–94. http://dx.doi.org/10.2478/cmam-2010-0004.

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AbstractThe present paper discusses the parallelization of the robust multigrid technique (RMT) and the possible way of applying this to unstructured grids. As opposed to the classical multigrid methods, the RMT is a trivial method of parallelization on coarse grids independent of the smoothing iterations. Estimates of the minimum speed-up and parallelism efficiency are given. An almost perfect load balance is demonstrated in a 3D illustrative test. To overcome the geometric nature of the technique, the RMT is used as a preconditioner in solving PDEs on unstructured grids. The procedure of auxiliary structured grids generation is considered in details.

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6

Cheng, Weijie, Renli Cheng, Jun Shi, Cong Zhang, Gaoxing Sun, and Dong Hua. "Interval Power Flow Analysis Considering Interval Output of Wind Farms through Affine Arithmetic and Optimizing-Scenarios Method." Energies 11, no. 11 (November 15, 2018): 3176. http://dx.doi.org/10.3390/en11113176.

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Wind power belongs to sustainable and clean energy sources which play a vital role of reducing environment pollution and addressing energy crisis. However, wind power outputs are quite difficult to predict because they are derived from wind speeds, which vary irregularly and greatly all the time. The uncertainty of wind power causes variation of the variables of power grids, which threatens the power grids’ operating security. Therefore, it is significant to provide the accurate ranges of power grids’ variables, which can be used by the operators to guarantee the power grid’s operating security. To achieve this goal, the present paper puts forward the interval power flow with wind farms model, where the generation power outputs of wind farms are expressed by intervals and three types of control modes are considered for imitating the operation features of wind farms. To solve the proposed model, the affine arithmetic-based method and optimizing-scenarios method are modified and employed, where three types of constraints of wind control modes are considered in their solution process. The former expresses the interval variables as affine arithmetic forms, and constructs optimization models to contract the affine arithmetic forms to obtain the accurate intervals of power flow variables. The latter regards active power outputs of the wind farms as variables, which vary in their corresponding intervals, and accordingly builds the minimum and maximum programming models for estimating the intervals of the power flow variables. The proposed methods are applied to two case studies, where the acquired results are compared with those acquired by the Monte Carlo simulation, which is a traditional method for handling interval uncertainty. The simulation results validate the advantages, effectiveness and the applicability of the two methods.

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7

Li, Chao, Tianguang Lu, and Xueshan Han. "Assessment method of large-scale distributed power consumption capacity for rural grids." Journal of Physics: Conference Series 2488, no. 1 (May 1, 2023): 012039. http://dx.doi.org/10.1088/1742-6596/2488/1/012039.

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Abstract As the scale of photovoltaic (PV) access continues to expand, both transmission and distribution grids are experiencing systemic consumption problems, with rural distribution grids being particularly prominent. An accurate assessment of distributed power consumption capacity is crucial to the improvement of distributed power consumption capacity. Firstly, taking into account the uncertainty of the output of the distributed power supply and comprehensive consideration of power quality, reliability of the electricity supply and operational influences, A comprehensive index evaluation system has been established to assess the ability of distributed power sources to consume; secondly, hierarchical analysis and improved gray correlation analysis are used to assign weights to the indexes; finally, a Monte Carlo model is used to identify the consumption capacity of rural power grids. This method can provide a comprehensive and accurate assessment of the consumption capacity of large-scale distributed power sources in new rural power grids, and also provide data support for solving the problem of new energy consumption in power grids.

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8

Liu, Wen Yang, and Wen Fu Zhang. "Split Rigidity Method for Analysis of Double-Layer Space Grids Structure with Rectangular Shape." Advanced Materials Research 446-449 (January 2012): 480–83. http://dx.doi.org/10.4028/www.scientific.net/amr.446-449.480.

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In this paper double-layer space grids structure with rectangular shape is assumed as equivalent sandwich plate, and has been analyzed by the non-traditional theory of plate with three generalized displacements, in which shearing deformation is considered. Based upon the split rigidity method, static analysis and natural vibration analysis of double-layer space grids structure has been studied. The formulas for calculating internal forces, displacement as well as fundamental frequency are given out. The comparison with finite element method and equivalent sandwich plate method shows that split rigidity method is not only simpler than other simplified methods but also of high accuracy.

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9

Liu, Wen Yang, and Wen Fu Zhang. "Split Rigidity Method for Analysis of Three-Way Double-Layer Space Grids Structure." Advanced Materials Research 594-597 (November 2012): 820–23. http://dx.doi.org/10.4028/www.scientific.net/amr.594-597.820.

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Abstract. In this paper three-way double-layer space grids structure is assumed as equivalent sandwich plate, and has been analyzed by the non-traditional theory of plate with three generalized displacements, in which shearing deformation is considered. Based upon the split rigidity method, static analysis and natural vibration analysis of three-way double-layer space grids structure has been studied. The formulas for calculating internal forces, displacement as well as natural vibration frequency are given out. The comparison with finite element method and equivalent sandwich plate method shows that the formulas in this paper are not only simpler than other simplified methods but also of high accuracy.

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10

Feng, Jian, Changtong Li, Yixiang Xu, Qian Zhang, Fang Wang, and Jianguo Cai. "Analysis of Key Elements of Truss Structures Based on the Tangent Stiffness Method." Symmetry 12, no. 6 (June 14, 2020): 1008. http://dx.doi.org/10.3390/sym12061008.

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In recent years, the topic of progressive structural collapse has received more attention around the world, and the study of element importance is the key to studying progressive collapse resistance. However, there are many elements in truss structures, making it difficult to predict their importance. The global stiffness matrix contains the specific information of the structure and singularity of the matrix can reflect the safety status of the structure, so it is useful to evaluate the key elements based on the global stiffness matrix for truss structures. In this paper, according to the tangent stiffness-based method for the element importance, the square pyramid grid was chosen as an example, and the distribution rules of key elements under different support conditions, stiffness distributions, and geometric parameters were studied. Then, three common symmetric grid forms, i.e., diagonal square pyramid grids, biorthogonal lattice grids, and biorthogonal diagonal lattice grids, were selected to investigate their importance indices of elements. The principle in this work can be utilized in progressive collapse analysis and safety assessment for spatial truss structures.

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11

Cai, Yumei, Zhengyu Liu, Zhao Dong, Benchao Liu, Yonghao Pang, and Jiawen Liu. "Forward Modeling Analysis of Cross-hole Resistivity Tomography (ERT) Using Unstructured Grids." Journal of Physics: Conference Series 2651, no. 1 (December 1, 2023): 012056. http://dx.doi.org/10.1088/1742-6596/2651/1/012056.

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Abstract The cross-hole electrical resistivity tomography (ERT) method has advantages in obtaining deep geological information and can accurately image complex underground structures. However, it is usually difficult to fit complex boundaries using structured grids in the modeling process. The accuracy of forward modeling is affected by the meshing of the model. The unstructured grids may describe the irregular complex model more effectively. Therefore, we study cross-hole ERT forward modeling, using unstructured grids to analyze the forward characteristics of complex underground structures. The effectiveness of the unstructured grids in cross-hole ERT has been revealed in this work.

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12

Ma, Hai-Ping, and Nik Norsyahariati Nik Daud. "Jointed Rock Failure Mechanism: A Method of Heterogeneous Grid Generation for DDARF." Applied Sciences 12, no. 12 (June 15, 2022): 6095. http://dx.doi.org/10.3390/app12126095.

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The original DDARF (discontinuous deformation analysis for rock failure) can only generate uniform grids, and the increase in the number of grids reduces the efficiency of calculation, which limits the use of DDARF in large-scale geotechnical engineering. This is a problem that needs to be solved in the original DDARF. A new method is proposed in this paper to optimize the generation of grids in DDARF, and the optimized DDARF can generate heterogeneous grids. The model of the Brazilian disc-splitting experiment was established by using the optimized DDARF, fine grids were generated in the crack propagation region of the model, andsparse grids were generated at the edge of the model. The simulation results show that the Brazilian disc-splitting experiment simulated by the optimized DDARF is more consistent with the physical experiment than the original DDARF. The optimized DDARF and the original DDARF were used to generate a heterogeneous grid model and a uniform grid model, respectively, to simulate the uniaxial compression experiment. Through the analysis of the experimental results, it can be concluded that the optimized DDARF is more accurate in simulating the cracking and propagation of joints in rock blocks, the results of optimized DDARF are more consistent with the simulation results of other software, and the computational efficiency of the optimized DDARF simulation experiment is much higher than that of the original DDARF at the same time.

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13

Flemisch, Bernd, and Barbara I. Wohlmuth. "A domain decomposition method on nested domains and nonmatching grids." Numerical Methods for Partial Differential Equations 20, no. 3 (2004): 374–87. http://dx.doi.org/10.1002/num.10095.

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14

Nikolova, N. K., H. W. Tam, and M. H. Bakr. "Sensitivity Analysis With the FDTD Method on Structured Grids." IEEE Transactions on Microwave Theory and Techniques 52, no. 4 (April 2004): 1207–16. http://dx.doi.org/10.1109/tmtt.2004.825710.

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15

Burton, Tristan M., and John K. Eaton. "Analysis of a Fractional-Step Method on Overset Grids." Journal of Computational Physics 177, no. 2 (April 2002): 336–64. http://dx.doi.org/10.1006/jcph.2002.7012.

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16

Gao, Yong Tao, and Xiao Hu. "Analysis on Integral Performance of Unit Glazing Curtain Wall Considering the Contribution of Glass Rigidity." Advanced Materials Research 163-167 (December 2010): 2454–58. http://dx.doi.org/10.4028/www.scientific.net/amr.163-167.2454.

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Based on integral property of unit glazing curtain wall (UGCW), considering the co-effect of glass and grids, set up the calculating method of cooperation of glass and grids; through the numerical simulation analysis with this method, we can conclude that take the glass’s rigidity into consideration is both reasonable and economical.

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17

Fukuyo, Kazuhiro. "Conditional stability of Larkin methods with non-uniform grids." Theoretical and Applied Mechanics 37, no. 2 (2010): 139–59. http://dx.doi.org/10.2298/tam1002139f.

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Stability analysis based on the von Neumann method showed that the Larkin methods for two-dimensional heat conduction with non- uniform grids are conditionally stable while they are known to be unconditionally stable with uniform grids. The stability criteria consisting of the dimensionless time step ?t, the space intervals ?x, ?y, and the ratios of neighboring space intervals ?, ? were derived from the stability analysis. A subsequent numerical experiment demonstrated that solutions derived by the Larkin methods with non-uniform grids lose stability and accuracy when the criteria are not satisfied.

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18

Chen, Wei Dong, Yan Chun Yu, Xian De Wu, Jian Cao Li, Ping Jia, and Feng Chao Zhang. "Application of Unstructured Finite Volume Method in Structural Static Mechanics." Key Engineering Materials 572 (September 2013): 273–76. http://dx.doi.org/10.4028/www.scientific.net/kem.572.273.

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Unstructured finite volume method applied in structural static mechanics has been discussed to direct at the difficulty of dealing with irregular boundary, unstructured triangle elements have been used in computational domain, the basic equations of unstructured finite volume method applied in structural static mechanics has been deduced. Comparing the unstructured grids with the structured grids, the former has obvious advantage on dealing with irregular boundary by theoretical analysis. According to examples analysis, the comparison of numeric results with analytic solutions and FEM solutions showed the effectiveness of the unstructured finite volume method.

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19

Adcock, Ben, and Rodrigo B. Platte. "A Mapped Polynomial Method for High-Accuracy Approximations on Arbitrary Grids." SIAM Journal on Numerical Analysis 54, no. 4 (January 2016): 2256–81. http://dx.doi.org/10.1137/15m1023853.

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20

Fornberg, Bengt. "High-Order Finite Differences and the Pseudospectral Method on Staggered Grids." SIAM Journal on Numerical Analysis 27, no. 4 (August 1990): 904–18. http://dx.doi.org/10.1137/0727052.

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21

Jimack, P. K., and A. J. Wathen. "Temporal Derivatives in the Finite-Element Method on Continuously Deforming Grids." SIAM Journal on Numerical Analysis 28, no. 4 (August 1991): 990–1003. http://dx.doi.org/10.1137/0728052.

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22

Wang, Jinxin, Yan Shi, Zilong Qin, Yihang Chen, and Zening Cao. "A Three-Dimensional Buffer Analysis Method Based on the 3D Discrete Global Grid System." ISPRS International Journal of Geo-Information 10, no. 8 (July 31, 2021): 520. http://dx.doi.org/10.3390/ijgi10080520.

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Three-dimensional (3D) buffer analysis is among the basic functions of 3D spatial analysis, and it plays an important role in 3D geographic information systems. The rapid development of the 3D Discrete Global Grid System (DGGS) provides a new method for the 3D spatial analysis of geographic information. According to the spatial topology characteristics of the 3D DGGS and the concept of dimensionality reduction, a 3D buffer analysis method based on the spatial grid of the Earth system is proposed to solve the problem of the buffer algorithm of a space object being unsatisfactory at present. In this paper, we present a method to calculate the distance between cells based on the side length of the spherical grids according to the geometric characteristics of the grids. For the grids of a geographic object, we describe the Euclidean distance expansion algorithm and the radial elevation expansion algorithm that helped us to obtain its 3D buffer. Finally, in terms of algorithm complexity and visualization effect, compared with the traditional raster buffer algorithm, the method presented in this paper has lower complexity, an improved visualization effect, and stronger generality.

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23

SU, HAOHANG, YIMEN ZHANG, YUMING ZHANG, and JINCAI MAN. "POWER GRIDS ANALYSIS IN COMPRESSED KRYLOV-SUBSPACE METHODS." Journal of Circuits, Systems and Computers 17, no. 03 (June 2008): 439–46. http://dx.doi.org/10.1142/s0218126608004435.

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An improved method is proposed based on compressed and Krylov-subspace iterative approaches to perform efficient static and transient simulations for large-scale power grid circuits. It is implemented with CG and BiCGStab algorithms and an excellent result has been obtained. Extensive experimental results on large-scale power grid circuits show that the present method is over 200 times faster than SPICE3 and around 10–20 times faster than ICCG method in transient simulations. Furthermore, the presented algorithm saves the memory usage over 95% of SPICE3 and 75% of ICCG method, respectively while the accuracy is not compromised.

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24

Buzzard, Gregery T., and Dongbin Xiu. "Variance-Based Global Sensitivity Analysis via Sparse-Grid Interpolation and Cubature." Communications in Computational Physics 9, no. 3 (March 2011): 542–67. http://dx.doi.org/10.4208/cicp.230909.160310s.

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AbstractThe stochastic collocation method using sparse grids has become a popular choice for performing stochastic computations in high dimensional (random) parameter space. In addition to providing highly accurate stochastic solutions, the sparse grid collocation results naturally contain sensitivity information with respect to the input random parameters. In this paper, we use the sparse grid interpolation and cubature methods of Smolyak together with combinatorial analysis to give a computationally efficient method for computing the global sensitivity values of Sobol’. This method allows for approximation of all main effect and total effect values from evaluation of f on a single set of sparse grids. We discuss convergence of this method, apply it to several test cases and compare to existing methods. As a result which may be of independent interest, we recover an explicit formula for evaluating a Lagrange basis interpolating polynomial associated with the Chebyshev extrema. This allows one to manipulate the sparse grid collocation results in a highly efficient manner.

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25

Liu, Wen Yang, and Wen Fu Zhang. "Split Rigidity Method for Analysis of Two-Way Orthogonal-Diagonal Double-Layer Space Grids Structure." Applied Mechanics and Materials 71-78 (July 2011): 306–9. http://dx.doi.org/10.4028/www.scientific.net/amm.71-78.306.

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In this paper two-way orthogonal-diagonal double-layer space grids structure is assumed as equivalent sandwich plate, and has been analyzed by the non-traditional theory of plate with three generalized displacements, in which shearing deformation is considered. Based upon the split rigidity method, static analysis and natural vibration analysis of two-way orthogonal-diagonal double-layer space grids structure has been studied and the simplified formulas are given out. The comparison with the results of equivalent sandwich plate method shows that as a more simplified method, split rigidity method is as accurate as equivalent sandwich plate method.

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26

Jiao, Bingqi, Zhicheng Xu, Kuan Zheng, Xiaoqing Yan, and Junshu Feng. "Evaluation method of clean power grid development mode." E3S Web of Conferences 236 (2021): 02002. http://dx.doi.org/10.1051/e3sconf/202123602002.

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In response to the climate change, it has been becoming the consensus of most countries in the world to accelerate the development of a high proportion of clean energy. The power grid is the core to support the development of a high proportion of clean energy, and the key is to accelerate the construction of clean power grids. This paper focuses on the main characteristics of clean power grid construction, and proposes a set of clean power grid development evaluation indicators including 5 first-level indicators and 19 second-level indicators and an analysis method based on radar charts. Taking China Power Grid as an example, this paper analyzes in detail the characteristics of the medium and long-term development mode of clean power grids and the relative change trends of specific indicators, and discusses the key links and potential problems that need attention in the development of clean power grids.

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27

Adetula, Bolade A., and Pavel M. Bokov. "Computational Method for Global Sensitivity Analysis of Reactor Neutronic Parameters." Science and Technology of Nuclear Installations 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/109614.

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The variance-based global sensitivity analysis technique is robust, has a wide range of applicability, and provides accurate sensitivity information for most models. However, it requires input variables to be statistically independent. A modification to this technique that allows one to deal with input variables that are blockwise correlated and normally distributed is presented. The focus of this study is the application of the modified global sensitivity analysis technique to calculations of reactor parameters that are dependent on groupwise neutron cross-sections. The main effort in this work is in establishing a method for a practical numerical calculation of the global sensitivity indices. The implementation of the method involves the calculation of multidimensional integrals, which can be prohibitively expensive to compute. Numerical techniques specifically suited to the evaluation of multidimensional integrals, namely, Monte Carlo and sparse grids methods, are used, and their efficiency is compared. The method is illustrated and tested on a two-group cross-section dependent problem. In all the cases considered, the results obtained with sparse grids achieved much better accuracy while using a significantly smaller number of samples. This aspect is addressed in a ministudy, and a preliminary explanation of the results obtained is given.

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28

Buranay, Suzan Cival, Ahmed Hersi Matan, and Nouman Arshad. "Two Stage Implicit Method on Hexagonal Grids for Approximating the First Derivatives of the Solution to the Heat Equation." Fractal and Fractional 5, no. 1 (February 26, 2021): 19. http://dx.doi.org/10.3390/fractalfract5010019.

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Анотація:

The first type of boundary value problem for the heat equation on a rectangle is considered. We propose a two stage implicit method for the approximation of the first order derivatives of the solution with respect to the spatial variables. To approximate the solution at the first stage, the unconditionally stable two layer implicit method on hexagonal grids given by Buranay and Arshad in 2020 is used which converges with Oh2+τ2 of accuracy on the grids. Here, h and 32h are the step sizes in space variables x1 and x2, respectively and τ is the step size in time. At the second stage, we propose special difference boundary value problems on hexagonal grids for the approximation of first derivatives with respect to spatial variables of which the boundary conditions are defined by using the obtained solution from the first stage. It is proved that the given schemes in the difference problems are unconditionally stable. Further, for r=ωτh2≤37, uniform convergence of the solution of the constructed special difference boundary value problems to the corresponding exact derivatives on hexagonal grids with order Oh2+τ2 is shown. Finally, the method is applied on a test problem and the numerical results are presented through tables and figures.

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29

BEGGAS, MOHAMMED, and MOHAMMED HAIOUR. "The Maximum Norm Analysis of Schwarz Method for Elliptic Quasi-Variational Inequalities." Kragujevac Journal of Mathematics 45, no. 4 (August 2021): 635–45. http://dx.doi.org/10.46793/kgjmat2104.635b.

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In this paper, we present a maximum norm analysis of an overlapping Schwartz method on non matching grids for a quasi-variational inequality, where the obstacle and the second member depend on the solution. Our result improves and generalizes some previous results.

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30

Steinbach, O. "A natural domain decomposition method with non-matching grids." Applied Numerical Mathematics 54, no. 3-4 (August 2005): 362–77. http://dx.doi.org/10.1016/j.apnum.2004.09.008.

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31

Pallav, R., and A. Pedas. "QUADRATIC SPLINE COLLOCATION METHOD FOR WEAKLY SINGULAR INTEGRAL EQUATIONS AND CORRESPONDING EIGENVALUE PROBLEM." Mathematical Modelling and Analysis 7, no. 2 (December 15, 2002): 285–96. http://dx.doi.org/10.3846/13926292.2002.9637200.

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Анотація:

A quadratic spline collocation method for the numerical solution of weakly singular Fredholm integral equations of the second kind and corresponding eigenvalue problem is constructed. Using quasi‐uniform and special graded grids, the rate of convergence of proposed numerical schemes is studied theoretically and numerically. Key words: weakly singular integral equations, collocation method, quadratic splines.

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32

Wakefield, Ron R., and Francis Tin-Loi. "Elastoplastic Analysis of Flat Grids Using Mathematical Programming." International Journal of Space Structures 4, no. 4 (December 1989): 228–34. http://dx.doi.org/10.1177/026635118900400404.

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This paper presents a method of analysing elastoplastic grids using a mathematical programming based formulation. The elastoplastic analysis is cast as a linear complementarity problem which can be efficiently solved by means of a scheme proposed by Kaneko. A computer program based on this scheme has been developed and can be used to analyse skeletal structures including grillages. The program's application is illustrated in this paper by performing the historical elastoplastic analysis of one of the grids tested at the University of Surrey.

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33

Gaspar, Francisco J., Francisco J. Lisbona, and Carmen Rodrigo. "MULTIGRID FOURIER ANALYSIS ON SEMI‐STRUCTURED ANISOTROPIC MESHES FOR VECTOR PROBLEMS." Mathematical Modelling and Analysis 15, no. 1 (February 15, 2010): 39–54. http://dx.doi.org/10.3846/1392-6292.2010.15.39-54.

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An efficient multigrid finite element method for vector problems on triangular anisotropic semi‐structured grids is proposed. This algorithm is based on zebra line‐type smoothers to overcome the difficulties arising when multigrid is applied on stretched meshes. In order to choose the type of multigrid cycle and the number of pre‐ and post‐smoothing steps, a three‐grid Fourier analysis is done. To this end, local Fourier analysis (LFA) on triangular grids for scalar problems is extended to the vector case. To illustrate the good performance of the method, a system of reaction‐diffusion is considered as model problem. A very satisfactory global convergence factor is obtained by using a V(0,2)‐cycle for domains triangulated with highly anisotropic meshes.

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Rosin, Argo, Imre Drovtar, Heigo Mõlder, Kaija Haabel, Victor Astapov, Toomas Vinnal, and Tarmo Korõtko. "Analysis of Traditional and Alternative Methods for Solving Voltage Problems in Low Voltage Grids: An Estonian Case Study." Energies 15, no. 3 (February 2, 2022): 1104. http://dx.doi.org/10.3390/en15031104.

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Smart Cities can benefit from existing municipal low voltage (LV) distribution grids by supporting public services with permanent power supply and providing grid connection points to distributed generators (DG). The increased integration of DGs and inverter based non-linear loads increases voltage quality issues, thus the cost-efficient assurance of voltage quality in LV grids with long radial lines is of increasing importance for the operators of municipal electricity distribution systems. Conventional methods for mitigating voltage quality issues (e.g., power line renovation) might not be optimal solutions either technologically or economically. Existing studies do not address all relevant issues related to the assurance of required voltage quality in such LV grids. This paper provides an overview of the applicability and rationality of traditional as well as alternative methods to solve voltage problems in LV grids. The authors use DIgSILENT PowerFactory software to simulate the performance of voltage stabilisers under different conditions. The authors propose a robust method for the classification of LV feeders and provide recommendations on how to resolve voltage quality problems, with the help of different power quality improvement devices, where the traditional methods of upgrading to medium voltage and grid reinforcement are economically infeasible. Based on our results, recommendations for mitigating voltage quality problems in LV distribution grids with radial lines of different lengths are given.

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35

Ambartsumyan, Ilona, Eldar Khattatov, Jan M. Nordbotten, and Ivan Yotov. "A Multipoint Stress Mixed Finite Element Method for Elasticity on Simplicial Grids." SIAM Journal on Numerical Analysis 58, no. 1 (January 2020): 630–56. http://dx.doi.org/10.1137/18m1229183.

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36

Misztal, Marek Krzysztof, Anier Hernandez-Garcia, Rastin Matin, Henning Osholm Sørensen, and Joachim Mathiesen. "Detailed analysis of the lattice Boltzmann method on unstructured grids." Journal of Computational Physics 297 (September 2015): 316–39. http://dx.doi.org/10.1016/j.jcp.2015.05.019.

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37

Hu, Fang Q., and Harold L. Atkins. "Eigensolution Analysis of the Discontinuous Galerkin Method with Nonuniform Grids." Journal of Computational Physics 182, no. 2 (November 2002): 516–45. http://dx.doi.org/10.1006/jcph.2002.7184.

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38

ZHAI, Jinjin, Yuantao SUN, Qing ZHANG, and Xianrong QIN. "Forming Analysis of Bulge Formed Joints Based on Adaptive Finite Element Method." Mechanics 27, no. 2 (April 15, 2021): 175–81. http://dx.doi.org/10.5755/j02.mech.24263.

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Metal bulk forming is widely used because of its own advantages. In order to improve the production efficiency and reduce the cost, numerical simulation is often used to analyze the volume forming process. Because of the large deformation and non-linearity of the forming process, the finite element method (FEM) has the problem of element distortion, which will affect the accuracy and even lead to the failure of the analysis process. In this paper, an adaptive finite element method (AFEM) is proposed to solve this problem. Firstly, the finite element model is established, and grids are roughly divided. After the analysis, according to the error calculation model, the area with large error is determined by the standard deviation of nominal strain energy of nodes. Then, the grids are refined by dichotomy method, and the calculation is continued, repeating this step until the error meets the requirement. Finally, the numerical analysis of the forging process of the bulge formed joint is taken as an example to prove the accuracy of the proposed method.

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39

Blomquist, Matthew, Scott R. West, Adam L. Binswanger, and Maxime Theillard. "Stable nodal projection method on octree grids." Journal of Computational Physics 499 (February 2024): 112695. http://dx.doi.org/10.1016/j.jcp.2023.112695.

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40

Vu, Anh Ngoc, and Tung Nguyen Minh Huynh. "An automated analysis process for vertical axis wind turbine." Science and Technology Development Journal 18, no. 4 (December 30, 2015): 145–52. http://dx.doi.org/10.32508/stdj.v18i4.1000.

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This paper presents an automated process for analyzing the performance of vertical axis wind turbine (VAWT). The details of this process will be demonstrated, which include the airfoil geometry representation using CST method, a hybrid meshing process combining structured grids and unstructured grids, CFD calculation process and processing data results to calculate the power coefficient of VAWT. These processes are designed as separate modules. CFD methods used in this research is RANS 2D using Realizable k  turbulence model. Meshing process will be done on the GAMBIT software, the CFD calculations are done on commercial ANSYS FLUENT software and these processes are controlled by mathematical software MATLAB. The formulas used to calculate the power coefficient will be also introduced in this paper.

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41

Farooqi, Muhammad Nufail, Daulet Izbassarov, Metin Muradoğlu, and Didem Unat. "Communication analysis and optimization of 3D front tracking method for multiphase flow simulations." International Journal of High Performance Computing Applications 33, no. 1 (March 15, 2017): 67–80. http://dx.doi.org/10.1177/1094342017694426.

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This paper presents a scalable parallelization of an Eulerian–Lagrangian method, namely the three-dimensional front tracking method, for simulating multiphase flows. Operating on Eulerian–Lagrangian grids makes the front tracking method challenging to parallelize and optimize because different types of communication (Lagrangian–Eulerian, Eulerian–Eulerian, and Lagrangian–Lagrangian) should be managed. In this work, we optimize the data movement in both the Eulerian and Lagrangian grids and propose two different strategies for handling the Lagrangian grid shared by multiple subdomains. Moreover, we model three different types of communication emerged as a result of parallelization and implement various latency-hiding optimizations to reduce the communication overhead. Good scalability of the parallelization strategies is demonstrated on two supercomputers. A strong scaling study using 256 cores simulating 1728 interfaces or bubbles achieves 32.5x speedup. We also conduct weak scaling study on 4096 cores simulating 27,648 bubbles on a 1024×1024×2048 Eulerian grid resolution.

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42

Kim, Seung-Jun, Young-Seok Choi, Yong Cho, Jong-Woong Choi, Jung-Jae Hyun, Won-Gu Joo, and Jin-Hyuk Kim. "Analysis of the Numerical Grids of a Francis Turbine Model through Grid Convergence Index Method." KSFM Journal of Fluid Machinery 23, no. 2 (April 30, 2020): 16–22. http://dx.doi.org/10.5293/kfma.2020.23.2.016.

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43

Sytova, S. "MULTICOMPONENT ITERATIVE METHOD FOR SOLVING TWO‐DIMENSIONAL HEAT TRANSFER EQUATION ON MOVING GRIDS." Mathematical Modelling and Analysis 5, no. 1 (December 15, 2000): 164–74. http://dx.doi.org/10.3846/13926292.2000.9637139.

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A multicomponent iterative method of domain decomposition on adaptive grids for solution of two‐dimensional heat transfer equation is proposed. The adaptive grid is constructed in curvilinear space where Cartesian grid is non‐stationary and depends on the solution behavior. In curvilinear space the initial two‐dimensional heat transfer equation is converted to the system of nonlinear parabolic equations with mixed derivatives, a source and convective transfer.

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44

Hesthaven, Jan S., and Fabian Mönkeberg. "Entropy stable essentially nonoscillatory methods based on RBF reconstruction." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 3 (May 2019): 925–58. http://dx.doi.org/10.1051/m2an/2019011.

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To solve hyperbolic conservation laws we propose to use high-order essentially nonoscillatory methods based on radial basis functions. We introduce an entropy stable arbitrary high-order finite difference method (RBF-TeCNOp) and an entropy stable second order finite volume method (RBF-EFV2) for one-dimensional problems. Thus, we show that methods based on radial basis functions are as powerful as methods based on polynomial reconstruction. The main contribution is the construction of an algorithm and a smoothness indicator that ensures an interpolation function which fulfills the sign-property on general one dimensional grids.

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45

Budd, Chris J., Weizhang Huang, and Robert D. Russell. "Adaptivity with moving grids." Acta Numerica 18 (May 2009): 111–241. http://dx.doi.org/10.1017/s0962492906400015.

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In this article we survey r-adaptive (or moving grid) methods for solving time-dependent partial differential equations (PDEs). Although these methods have received much less attention than their h- and p-adaptive counterparts, particularly within the finite element community, we review the substantial progress that has been made in developing more robust and reliable algorithms and in understanding the basic principles behind these methods, and we give some numerical examples illustrative of the wide classes of problems for which these methods are suitable alternatives to the traditional ones.More specifically, we first examine the basic geometric properties of moving meshes in both one and higher spatial dimensions, and discuss the discretization process for PDEs on such moving meshes (both structured and unstructured). In particular, we consider the issues of mesh regularity, equidistribution, alignment, and associated variational methods. An overview is given of the general interpolation error analysis for a function or a truncation error on such an adaptive mesh. Guided by these principles, we show how to design effective moving mesh strategies. We then examine in more detail how these strategies can be implemented in practice. The first class of methods which we consider are based upon controlling mesh density and hence are called position-based methods. These make use of a so-called moving mesh PDE (MMPDE) approach and variational methods, as well as optimal transport methods. This is followed by an analysis of methods which have a more Lagrange-like interpretation, and due to this focus are called velocity-based methods. These include the moving finite element method (MFE), the geometric conservation law (GCL) methods, and the deformation map method. Finally, we present a number of specific types of examples for which the use of a moving mesh method is particularly effective in applications. These include scale-invariant problems, blow-up problems, problems with moving fronts and problems in meteorology. We conclude that, whilst r-adaptive methods are still in their relatively early stages of development, with many outstanding questions remaining, they have enormous potential and indeed can produce an optimal form of adaptivity for many problems.

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46

Chou, So-Hsiang, Songnian He, and Wen-Wei Lin. "Conservative flux recovery from theQ1 conforming finite element method on quadrilateral grids." Numerical Methods for Partial Differential Equations 20, no. 1 (2003): 104–27. http://dx.doi.org/10.1002/num.10084.

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47

Rösch, Tobias, and Peter Treffinger. "Cluster Analysis of Distribution Grids in Baden-Württemberg." Energies 12, no. 20 (October 22, 2019): 4016. http://dx.doi.org/10.3390/en12204016.

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With the growing share of renewable energies in the electricity supply, transmission and distribution grids have to be adapted. A profound understanding of the structural characteristics of distribution grids is essential to define suitable strategies for grid expansion. Many countries have a large number of distribution system operators (DSOs) whose standards vary widely, which contributes to coordination problems during peak load hours. This study contributes to targeted distribution grid development by classifying DSOs according to their remuneration requirement. To examine the amendment potential, structural and grid development data from 109 distribution grids in South-Western Germany, are collected, referring to publications of the respective DSOs. The resulting data base is assessed statistically to identify clusters of DSOs according to the fit of demographic requirements and grid-construction status and thus identify development needs to enable a broader use of regenerative energy resources. Three alternative algorithms are explored to manage this task. The study finds the novel Gauss-Newton algorithm optimal to analyse the fit of grid conditions to regional requirements and successfully identifies grids with remuneration needs. It is superior to the so far used K-Means algorithm. The method developed here is transferable to other areas for grid analysis and targeted, cost-efficient development.

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48

Zhang, Wensheng, and Hui Zheng. "A multiscale method for wave propagation in 3D heterogeneous poroelastic media." GEOPHYSICS 84, no. 4 (July 1, 2019): T237—T257. http://dx.doi.org/10.1190/geo2018-0482.1.

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A new multiscale method for wave simulation in 3D heterogeneous poroelastic media is developed. Wave propagation in inhomogeneous media involves many different scales of media. The physical parameters in the real media usually vary greatly within a very small scale. For the direct numerical methods for wave simulation, a refined grid is required in mesh generation to maintain the match between the mesh size and the material variations in the spatial scale. This greatly increases the computational cost and computer memory requirements. The multiscale method can overcome this difficulty due to the scale difference. The basic idea of our multiscale method is to construct computational schemes on two sets of meshes, i.e., coarse grids and fine grids. The finite-volume method is applied on the coarse grids, whereas the multiscale basis functions are computed with the finite-element method by solving a local problem on the fine grids. Moreover, the local problem only needs to be solved once before time stepping. This allows us to use a coarse grid while still capturing the information of the physical property variations in the small scale. Therefore, it has better accuracy than the single-scale method when they use the same coarse grids. The theoretical method and the dispersion analysis are investigated. Numerical computations with the perfectly matched layer boundary conditions are completed for 3D inhomogeneous poroelastic models with randomly distributed small scatterers. The results indicate that our multiscale method can effectively simulate wave propagation in 3D heterogeneous poroelastic media with a significant reduction in computation cost.

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49

Purna Prakash, Kasaraneni, Yellapragada Venkata Pavan Kumar, Kasaraneni Himajyothi, and Gogulamudi Pradeep Reddy. "Comprehensive Bibliometric Analysis on Smart Grids: Key Concepts and Research Trends." Electricity 5, no. 1 (February 1, 2024): 75–92. http://dx.doi.org/10.3390/electricity5010005.

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Over the years, a rapid evolution of smart grids has been witnessed across the world due to their intelligent operations and control, smart characteristics, and benefits, which can overcome several difficulties of traditional electric grids. However, due to multifaceted technological advancements, the development of smart grids is evolving day by day. Thus, smart grid researchers need to understand and adapt to new concepts and research trends. Understanding these new trends in smart grids is essential for several reasons, as the energy sector undergoes a major transformation towards becoming energy efficient and resilient. Moreover, it is imperative to realize the complete potential of modernizing the energy infrastructure. In this regard, this paper presents a comprehensive bibliometric analysis of smart grid concepts and research trends. In the initial search, the bibliometric data extracted from the Scopus and Web of Science databases totaled 11,600 and 2846 records, respectively. After thorough scrutiny, 2529 unique records were considered for the bibliometric analysis. Bibliometric analysis is a systematic method used to analyze and evaluate the scholarly literature on a particular topic and provides valuable insights to researchers. The proposed analysis provides key information on emerging research areas, high-impact sources, authors and their collaboration, affiliations, annual production of various countries and their collaboration in smart grids, and topic-wise title count. The information extracted from this bibliometric analysis will help researchers and other stakeholders to thoroughly understand the above-mentioned aspects related to smart grids. This analysis was carried out on smart grid literature by using the bibliometric package in R.

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50

Kangro, R., and I. Kangro. "ON THE STABILITY OF PIECEWISE POLYNOMIAL COLLOCATION METHODS FOR SOLVING WEAKLY SINGULAR INTEGRAL EQUATIONS OF THE SECOND KIND." Mathematical Modelling and Analysis 13, no. 1 (March 31, 2008): 29–36. http://dx.doi.org/10.3846/1392-6292.2008.13.29-36.

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Piecewise polynomial collocation methods on special nonuniform grids are efficient methods for solving weakly singular Fredholm and Volterra integral equations but there is a widespread belief that those methods are numerically unstable in the case of large values of the nonuniformity parameter r. We show that this method by itself is stable and discuss some implementation problems that may lead to unstable behavior of numerical results.

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