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Journal articles on the topic 'Triangular splitting'

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Author: Grafiati

Published: 10 March 2023

Last updated: 11 March 2023

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1

Hahmann, Stefanie, and Georges-Pierre Bonneau. "Triangular G1 interpolation by 4-splitting domain triangles." Computer Aided Geometric Design 17, no. 8 (September 2000): 731–57. http://dx.doi.org/10.1016/s0167-8396(00)00021-2.

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2

Grosso, G., G. Pastori Parravicini, and C. Piermarocchi. "Valley splitting in triangular Si(001) quantum wells." Physical Review B 54, no. 23 (December 15, 1996): 16393–96. http://dx.doi.org/10.1103/physrevb.54.16393.

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3

Zhang, Ling, Xingyue Wang, Ang Li, Xingqun Zheng, Lishan Peng, Jiawei Huang, Zihua Deng, Hongmei Chen, and Zidong Wei. "Rational construction of macroporous CoFeP triangular plate arrays from bimetal–organic frameworks as high-performance overall water-splitting catalysts." Journal of Materials Chemistry A 7, no. 29 (2019): 17529–35. http://dx.doi.org/10.1039/c9ta05282h.

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4

Ridouane, El Hassan, and Antonio Campo. "Heightened Thermal Convection as a Result of Splitting a Square Cavity Diagonally in Half." Journal of Electronic Packaging 128, no. 3 (August 9, 2005): 251–58. http://dx.doi.org/10.1115/1.2229224.

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This investigation addresses the thermogeometric performance of a two-square cavity system contrasted against a two-isosceles triangular cavity system, with an exactly equal heating segment and comparable cooling segment. When one square cavity is cut diagonally in half, it results in a pair of isosceles triangular cavities. The isosceles triangular cavity on the left is heated from the left vertical wall, the top wall is insulated, and the inclined wall is cold; the so-called HIC triangular cavity. The isosceles triangular cavity on the right is heated from the right vertical wall, the bottom wall is insulated, and the inclined wall is cold; the so-called HCI triangular cavity. It may be speculated that the two-isosceles triangular cavity system may find application in the miniaturization of electronic packaging severely constrained by space and/or weight. The finite volume method, accounting for temperature-dependent thermophysical properties of air, is employed to perform the computational analysis. Representative height-based Rayleigh numbers assume values up to 106 to avoid oscillations that occur at a Rayleigh number between RaH=2×106 and 2.2×106. Numerical results are reported for the velocity field, the temperature field, and the local and the mean convective coefficient along the heated vertical wall. Under a dominant conduction condition for RaH=103, the heat flux across the derived two-isosceles triangular system is 334% higher than its counterpart across the original two-square system. In contrast, for a dominant convection condition for RaH=106, this margin diminishes to 20%, but still constitutes a significant improvement. For the design of two-triangular cavity systems, a NuH correlation equation has been constructed yielding a maximum error of 2% at RaH=104.

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5

BAKSHEYEV, D. G., A. A. BYKOV, V. A. TKACHENKO, O. A. TKACHENKO, L. V. LITVIN, A. V. LATYSHEV, A. L. ASEEV, O. ESTIBALS, and J. C. PORTAL. "COULOMB INTERACTION OF TRIANGULAR QUANTUM DOTS IN A SMALL RING INTERFEROMETER." International Journal of Nanoscience 02, no. 06 (December 2003): 495–503. http://dx.doi.org/10.1142/s0219581x03001607.

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Doublet splitting of single-electron peaks has been observed in the conductance of a small high-resistance ring interferometer. Realistic modeling of the device shows that the electron system of interferometer divides into two triangular quantum dots connected by single-mode channels to each other and to reservoirs. We explain the splitting of conductance peaks by charge interaction of the dots.

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6

Cowan, Richard. "A mosaic of triangular cells formed with sequential splitting rules." Journal of Applied Probability 41, A (2004): 3–15. http://dx.doi.org/10.1239/jap/1082552186.

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The iterative division of a triangle by chords which join a randomly-selected vertex of a triangle to the opposite side is investigated. Results on the limiting random graph which eventuates are given. Aspects studied are: the order of vertices; the fragmentation of chords; age distributions for elements of the graph; various topological characterisations of the triangles. Different sampling protocols are explored. Extensive use is made of the theory of branching processes.

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7

Kohler, A., G. H. M. Killesreiter, and R. Blümel. "Ray splitting in a class of chaotic triangular step billiards." Physical Review E 56, no. 3 (September 1, 1997): 2691–701. http://dx.doi.org/10.1103/physreve.56.2691.

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8

Cowan, Richard. "A mosaic of triangular cells formed with sequential splitting rules." Journal of Applied Probability 41, A (2004): 3–15. http://dx.doi.org/10.1017/s0021900200112161.

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The iterative division of a triangle by chords which join a randomly-selected vertex of a triangle to the opposite side is investigated. Results on the limiting random graph which eventuates are given. Aspects studied are: the order of vertices; the fragmentation of chords; age distributions for elements of the graph; various topological characterisations of the triangles. Different sampling protocols are explored. Extensive use is made of the theory of branching processes.

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9

Zheng, Qing-Qing, and Chang-Feng Ma. "A class of triangular splitting methods for saddle point problems." Journal of Computational and Applied Mathematics 298 (May 2016): 13–23. http://dx.doi.org/10.1016/j.cam.2015.11.026.

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10

Muratova, Galina, Tatiana Martynova, Evgeniya Andreeva, Vadim Bavin, and Zeng-Qi Wang. "Numerical Solution of the Navier–Stokes Equations Using Multigrid Methods with HSS-Based and STS-Based Smoothers." Symmetry 12, no. 2 (February 4, 2020): 233. http://dx.doi.org/10.3390/sym12020233.

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Multigrid methods (MGMs) are used for discretized systems of partial differential equations (PDEs) which arise from finite difference approximation of the incompressible Navier–Stokes equations. After discretization and linearization of the equations, systems of linear algebraic equations (SLAEs) with a strongly non-Hermitian matrix appear. Hermitian/skew-Hermitian splitting (HSS) and skew-Hermitian triangular splitting (STS) methods are considered as smoothers in the MGM for solving the SLAE. Numerical results for an algebraic multigrid (AMG) method with HSS-based smoothers are presented.

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11

Narayan, J. P., and A. Kumar. "Quantification of Effects of Ridge and Valley Topography on the Rayleigh Wave Characteristics." Journal of Earthquake and Tsunami 12, no. 03 (August 12, 2018): 1850007. http://dx.doi.org/10.1142/s1793431118500070.

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The effects of ridge and valley on the characteristics of Rayleigh waves are presented in this paper. The research work carried out has been stimulated by the day by day increase of long-span structures in the hilly areas which are largely affected by the spatial variability in ground motion caused by the high-frequency Rayleigh waves. The Rayleigh wave responses of the considered triangular and elliptical ridge and valley models were computed using a fourth-order accurate staggered-grid viscoelastic P-SV wave finite-difference (FD) program. The simulated results revealed very large amplification of the horizontal component and de-amplification of the vertical component of Rayleigh wave at the top of a triangular ridge and de-amplification of both the components at the base of the triangular valley. The observed amplification of both the components of Rayleigh wave in front of elliptical valley was larger than triangular valley models. A splitting of the Rayleigh wave wavelet was inferred after interaction with ridge and valley. It is concluded that the large-scale topography acts as a natural insulator for the surface waves and the insulating capacity of the valley is more than that of a ridge. This insulation phenomenon is arising due to the reflection, diffraction and splitting of the surface wave while moving across the topography. It is concluded that insulating potential of the topography for the Rayleigh waves largely depends on their shape and shape-ratio.

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12

Klochkov, Yuriy V., Anatoliy P. Nikolaev, and Olga V. Vakhnina. "Numerical analysis of the stress-strain state of thin shells based on a joint triangular finite element." Structural Mechanics of Engineering Constructions and Buildings 15, no. 2 (December 15, 2019): 117–26. http://dx.doi.org/10.22363/1815-5235-2019-15-2-117-126.

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Relevance. The use of the finite element method for determining the stressstrain state of thin-walled elements of engineering structures predetermines their discretization into separate finite elements. Splitting irregular parts of the structure is impossible without the use of triangular areas. The triangular elements of shell structures are joint in displacements and in their derivatives only at the nodal points. Therefore, ways to improve the compatibility conditions at the boundaries of triangular elements are relevant. Aims of research. The aim of the work is to improve the compatibility conditions at the boundaries of adjacent triangular elements based on equating the derivatives of normal displacements in the middle of the boundary sides. Methods. In order to improve the compatibility conditions at the boundaries of triangular elements in this work, the Lagrange functional is used with the condition of ensuring equality in the middle of the sides of adjacent elements derived from normal displacements in the directions of perpendiculars tangent to the middle surface of the shell. Results. Using the example of analysing an elliptical shell, the efficiency of using a joint triangular finite element is shown, whose stiffness matrix is formed in accordance with the algorithm outlined in this article.

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13

Zhou, Sheng-Wei, Ai-Li Yang, and Yu-Jiang Wu. "A relaxed block-triangular splitting preconditioner for generalized saddle-point problems." International Journal of Computer Mathematics 94, no. 8 (September 3, 2016): 1609–23. http://dx.doi.org/10.1080/00207160.2016.1226500.

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14

Zhou, Sheng-Wei, Ai-Li Yang, and Yu-Jiang Wu. "Two modified block-triangular splitting preconditioners for generalized saddle-point problems." Computers & Mathematics with Applications 74, no. 6 (September 2017): 1176–97. http://dx.doi.org/10.1016/j.camwa.2017.06.004.

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15

Gong, Chunye, Weimin Bao, Guojian Tang, Changwan Min, and Jie Liu. "An Efficient Iteration Method for Toeplitz-Plus-Band Triangular Systems Generated from Fractional Ordinary Differential Equation." Mathematical Problems in Engineering 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/194249.

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It is time consuming to numerically solve fractional differential equations. The fractional ordinary differential equations may produce Toeplitz-plus-band triangular systems. An efficient iteration method for Toeplitz-plus-band triangular systems is presented withOMlogMcomputational complexity andOMmemory complexity in this paper, compared with the regular solution withOM2computational complexity andOM2memory complexity.Mis the discrete grid points. Some methods such as matrix splitting, FFT, compress memory storage and adjustable matrix bandwidth are used in the presented solution. The experimental results show that the presented method compares well with the exact solution and is 4.25 times faster than the regular solution.

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16

Luo, Jia-Min, Hou-Biao Li, and Wei-Bo Wei. "Block splitting preconditioner for time-space fractional diffusion equations." Electronic Research Archive 30, no. 3 (2022): 780–97. http://dx.doi.org/10.3934/era.2022041.

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<abstract><p>For solving a block lower triangular Toeplitz linear system arising from the time-space fractional diffusion equations more effectively, a single-parameter two-step split iterative method (TSS) is introduced, its convergence theory is established and the corresponding preconditioner is also presented. Theoretical analysis shows that the original coefficient matrix after preconditioned can be expressed as the sum of the identity matrix, a low-rank matrix, and a small norm matrix. Numerical experiments show that the preconditioner improve the calculation efficiency of the Krylov subspace iteration method.</p></abstract>

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17

Salmi, Ebrahim Fathi, and Saeed Hosseinzadeh. "A Further Study on the Mechanism of Pre-Splitting in Mining Engineering." Applied Mechanics and Materials 553 (May 2014): 476–81. http://dx.doi.org/10.4028/www.scientific.net/amm.553.476.

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In this paper, the mechanism of pre-splitting was analysed using both theoretical and numerical methods. An analytical approach was derived based on the thick-wall cylinder theory. Numerical simulation of pre-split blasting of a two adjacent blast-hole bench was conducted using FLAC3Dsoftware. The sequential loading stages of explosive and stress wave were simplified to a triangular shape pulse and applied to the inner wall of blast-holes. Blast wave fronts and plastic zones were monitored in different elapsed times after detonation. Numerical findings show that collision between the two adjacent stress waves induces a tensile wave, playing the key role in pre-splitting.

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18

Phongthanapanich, Sutthisak. "Multidimensional Dissipation Technique for Roe's Flux-Difference Splitting Scheme on Triangular Grids." Engineering Journal 14, no. 2 (April 29, 2010): 33–40. http://dx.doi.org/10.4186/ej.2010.14.2.33.

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19

Wen, Chun, Ting-Zhu Huang, and Chao Wang. "Triangular and skew-symmetric splitting method for numerical solutions of Markov chains." Computers & Mathematics with Applications 62, no. 11 (December 2011): 4039–48. http://dx.doi.org/10.1016/j.camwa.2011.09.041.

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20

Li, Jing-Tao, and Chang-Feng Ma. "The parameterized upper and lower triangular splitting methods for saddle point problems." Numerical Algorithms 76, no. 2 (January 11, 2017): 413–25. http://dx.doi.org/10.1007/s11075-017-0263-7.

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21

Bai, Zhong-Zhi, Gene H. Golub, Lin-Zhang Lu, and Jun-Feng Yin. "Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems." SIAM Journal on Scientific Computing 26, no. 3 (January 2005): 844–63. http://dx.doi.org/10.1137/s1064827503428114.

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22

Krukier, Lev A., Boris L. Krukier, and Zhi-Ru Ren. "Generalized skew-Hermitian triangular splitting iteration methods for saddle-point linear systems." Numerical Linear Algebra with Applications 21, no. 1 (January 25, 2013): 152–70. http://dx.doi.org/10.1002/nla.1870.

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23

Stoufflet, Bruno. "Investigation of generalized flux vector splitting for compressible flows on triangular meshes." International Journal for Numerical Methods in Fluids 20, no. 8-9 (April 30, 1995): 1047–59. http://dx.doi.org/10.1002/fld.1650200822.

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24

Cui, Jingjing, Guohua Peng, Quan Lu, and Zhengge Huang. "A new two-step iteration method for discrete ill-posed problems and image restoration." Filomat 36, no. 6 (2022): 1837–55. http://dx.doi.org/10.2298/fil2206837c.

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In this study, for the augmented linear system of discrete ill-posed problems we establish a new two-step (NTS) iteration method containing a parameter and a parameter matrix, which is based on the Hermitian and skew-Hermitian splitting (HSS) and the upper and lower triangular splitting (ULT) of the coefficient matrix. Then, we theoretically study its convergence properties and determine its optimal iteration parameters. It is seen that the NTS method converges faster when the parameters are chosen properly. Experimental examples are carried out to further validate the effectiveness and accuracy of the new method compared to the newly developed methods in terms of the numerical performance and image recovering quality.

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25

Fan, Hong-Tao, Mehdi Bastani, Bing Zheng, and Xin-Yun Zhu. "A class of upper and lower triangular splitting iteration methods for image restoration." Applied Mathematical Modelling 54 (February 2018): 82–111. http://dx.doi.org/10.1016/j.apm.2017.09.033.

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26

Phongthanapanich, Sutthisak, and Pramote Dechaumphai. "Healing of shock instability for Roe's flux-difference splitting scheme on triangular meshes." International Journal for Numerical Methods in Fluids 59, no. 5 (February 20, 2009): 559–75. http://dx.doi.org/10.1002/fld.1834.

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27

Cheng, Chia-Hsin, and Yi Yan. "Indoor positioning system for wireless sensor networks based on two-stage fuzzy inference." International Journal of Distributed Sensor Networks 14, no. 5 (May 2018): 155014771878064. http://dx.doi.org/10.1177/1550147718780649.

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Wireless indoor positioning systems are susceptible to environmental distortion and attenuation of the signal, which can affect positioning accuracy. In this article, we present a two-stage indoor positioning scheme using a fuzzy-based algorithm aimed at minimizing uncertainty in received signal strength indicator measures from reference nodes in wireless sensor networks. In the first stage, the indoor space is divided into several zones and a fuzzy-based indoor zone-positioning scheme is used to identify the zone in which the target node is located via zone splitting. In the second stage, adaptive trilateration is used to position the target node within the zone identified in the first stage. Simulation results demonstrate that the proposed two-stage fuzzy rectangular splitting outperforms non-fuzzy-based algorithms, including K-Nearest Neighbors–based localization, and traditional triangular splitting schemes. We also developed an expanded positioning scheme to facilitate the selection of a positioning map for large indoor spaces, thereby overcoming the limitations imposed by the size of the positioning area while maintaining high positioning resolution.

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28

Lu, Jun-Feng. "The ULT-HSS hybrid iteration method for symmetric saddle point problems." Thermal Science 25, no. 3 Part B (2021): 2377–84. http://dx.doi.org/10.2298/tsci200115128l.

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This paper proposes a hybrid iteration method for solving symmetric saddle point problem arising in CFD. It is an implicit alternative direction iteration method and named as the ULT-HSS (upper and lower triangular, Hermitian and skew- Hermitian splitting) method. The convergence analysis is provided, and the necessary and sufficient conditions are given for the convergence of the method. Some practical approaches are formulated for setting the optimal parameter of the method. Numerical experiments are given to show its efficiency.

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29

Volk, O. H., and S. M. Perold. "Studies in the genus Riccia (Marchantiales) from southern Africa. 6. R. hirsuta, a new species, in a new section." Bothalia 16, no. 2 (October 28, 1986): 187–91. http://dx.doi.org/10.4102/abc.v16i2.1086.

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Riccia hirsuta Volk Perold, sp. nov., the type species of a new section, Micantes Volk Perold, subgenus Spongodes (Nees) Volk is described. It is characterized by tall, dorsal, hair-like, multi-cellular outgrowths from an epidermis with distant air-pores, leading to polyhedral air-chambers below, and is the only species in this subgenus with these outgrowths. The ventral scales are triangular, apically splitting into long, hair-like appendages. This species is endemic to the north-west and central Cape Province.

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30

Wang, Bin. "Triangular splitting implementation of RKN‐type Fourier collocation methods for second‐order differential equations." Mathematical Methods in the Applied Sciences 41, no. 5 (January 9, 2018): 1998–2011. http://dx.doi.org/10.1002/mma.4727.

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31

Cheng, Guo, and Ji-Cheng Li. "A relaxed upper and lower triangular splitting preconditioner for the linearized Navier–Stokes equation." Computers & Mathematics with Applications 80, no. 1 (July 2020): 43–60. http://dx.doi.org/10.1016/j.camwa.2020.02.025.

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32

Avinash, K. G., and I. S. Rao. "Highly Selective Dual-Mode Microstrip Bandpass Filters Using Triangular Patch Resonators." Advanced Electromagnetics 6, no. 1 (March 11, 2017): 77. http://dx.doi.org/10.7716/aem.v6i1.469.

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In this paper, highly selective dual-mode microstrip bandpass filters are proposed using horizontal and vertical slots formed on the surface of a triangular patch. Slots are responsible for splitting and coupling of dual degenerate modes and also facilitate in controlling their resonant frequencies by varying the dimensions of the slots. Horizontal and vertical slots reroute the direction of the flow of current on the surface of the patch, which results in switching of transmission zeros. Two 2-pole and one 4-pole dual-mode filters are designed, simulated and fabricated. Two pole filters have transmission zeros on side of the passband and four pole filter have transmission zeros on both sides of the passband. The designed filters exhibit a fractional bandwidth of less than 7 % and there is a good agreement between simulated and measured results.

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33

Zhu, J., K. Zong, F. Goudail, N. Zhang, and X. Hou. "ERROR ANALYSIS OF THE DISPERSION-COMPENSATED WIDE-BAND POLARIZATION SAGNAC INTERFEROMETER." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLIII-B1-2020 (August 6, 2020): 621–25. http://dx.doi.org/10.5194/isprs-archives-xliii-b1-2020-621-2020.

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Abstract. Imaging polarimetry can obtain two-dimensional intensity distribution information and its corresponding states of polarization from the target simultaneously. Sagnac polarization imaging interferometer is one of the typical channeled polarimetry technologies. By splitting the incident light through the triangular optical structure, the polarization information of the target is modulated into the interference fringes and can be obtained by the demodulation algorithm. The non-ideal optical elements in the system will cause reconstruction errors. This article analyses several factors that affect the measurement accuracy, including the splitting ratio of polarization beam splitter and the diffraction efficiency of the blazed grating. We derive the modified intensity formula and obtain interference patterns through numerical simulations. By calculating the modulation degree of interference fringes and reconstruction error under different non-ideal parameters, we have come to the conclusion that to meet the requirement of modulation degree > 0.5 and reconstruction error < 10%, the beam splitting ratio of the PBS should be α < 1.22. The diffraction efficiency ratio of s-polarization to p-polarization of the blazed grating should be ηs/ηp > 0.83, and the first-order diffraction efficiency should be η1 > 79%.

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34

Raicevic, Nevena, and Milan Tadic. "Influence of strain on band structure of semiconductor nanostructures." Serbian Journal of Electrical Engineering 6, no. 3 (2009): 461–69. http://dx.doi.org/10.2298/sjee0903461r.

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The influence of the mechanical strain on the electronic structure of the asymmetric (In,Ga)As/GaAs quantum well is considered. Both the direct influence of strain on the orbital part of the electronic structure and an indirect influence through the strain dependent Rashba and Dresselhaus Hamiltonians are taken into account. The analyzed quantum well is taken to have a triangular shape, and is oriented along the <110> direction. For this direction, there exists both the intrinsic and strain-induced spin-orbit interaction. For all analyzed types of spin-orbit interaction, subband splittings depend linearly on the in-plane wave vector. On the other hand, the electronic structure for the Rashba type of the strain-induced spin-orbit interaction shows isotropic dependence in the k-space, while the electronic structure due to the Dresselhaus type shows anisotropy. Furthermore, the Rashba strain-induced spin-orbit interaction increases subband splitting, while the effect of the Dresselhaus Hamiltonian on the electronic structure is opposite to the intrinsic spin-orbit interaction for certain polar angles.

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35

SADEL, CHRISTIAN, and DISHENG XU. "Singular analytic linear cocycles with negative infinite Lyapunov exponents." Ergodic Theory and Dynamical Systems 39, no. 4 (August 17, 2017): 1082–98. http://dx.doi.org/10.1017/etds.2017.52.

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We show that linear analytic cocycles where all Lyapunov exponents are negative infinite are nilpotent. For such one-frequency cocycles we show that they can be analytically conjugated to an upper triangular cocycle or a Jordan normal form. As a consequence, an arbitrarily small analytic perturbation leads to distinct Lyapunov exponents. Moreover, in the one-frequency case where the $k$th Lyapunov exponent is finite and the $(k+1)$st negative infinite, we obtain a simple criterion for domination in which case there is a splitting into a nilpotent part and an invertible part.

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36

Sun, Fu Ting, Qing Ren Jiang, and Cheng Xue She. "Research on Three-Dimensional Roughness Characteristics of Tensile Granite Joint." Applied Mechanics and Materials 204-208 (October 2012): 514–19. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.514.

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The three-dimensional roughness characteristics of the tensile granite joint surfaces are studied. Firstly, the tensile granite joints are prepared by splitting cubic granite blocks, and the triangular networks of the joint surfaces are established based on the topographic data collected by laser scanner. Then, the roughness characteristics of the two-dimensional profiles in different positions and different directions are studied. It proves that the roughness of the tensile granite joint surface is position and direction depended, and the roughness parameters based on the profiles are inadequate to characterize the roughness of the three-dimensional joint surfaces. Some new roughness parameters to characterize the three-dimensional joint surfaces are finally calculated on the basis of the triangular networks, these parameters can reflect the spatial and anisotropic characteristics of the joint surfaces. The results in this paper will lay the foundation for further study of the roughness characteristics and mechanical properties of the tensile rock joints.

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37

Zhang, Jianhua, Zewen Wang, and Jing Zhao. "Preconditioned symmetric block triangular splitting iteration method for a class of complex symmetric linear systems." Applied Mathematics Letters 86 (December 2018): 95–102. http://dx.doi.org/10.1016/j.aml.2018.06.024.

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38

TRÉPANIER, J. ‐Y, M. REGGIO, and D. AIT‐ALI‐YAHIA. "AN IMPLICIT FLUX‐DIFFERENCE SPLITTING METHOD FOR SOLVING THE EULER EQUATIONS ON ADAPTIVE TRIANGULAR GRIDS." International Journal of Numerical Methods for Heat & Fluid Flow 3, no. 1 (January 1993): 63–77. http://dx.doi.org/10.1108/eb017516.

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39

Dang, Rui, Xiu-feng Xu, and Meng-meng Xie. "Fabrication of triangular Cu3P nanorods on Cu nanosheets as electrocatalyst for boosted electrocatalytic water splitting." Journal of Central South University 29, no. 12 (December 2022): 3870–83. http://dx.doi.org/10.1007/s11771-023-5243-6.

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40

Phongthanapanich, Sutthisak. "Healing of the Carbuncle Phenomenon for AUSMDV Scheme on Triangular Grids." International Journal of Nonlinear Sciences and Numerical Simulation 17, no. 1 (February 1, 2016): 15–28. http://dx.doi.org/10.1515/ijnsns-2015-0008.

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AbstractThe carbuncle phenomenon, commonly occurring in solutions of compressible Euler equations, is a numerical instability associated with shock-induced anomalies. It is associated with several shock-capturing finite-volume methods designed to preserve the contact discontinuities. Due to the lack of theoretical knowledge of the carbuncle phenomenon, it is not known which numerical scheme is affected or under what circumstances that the phenomenon occur. The objective of this article is to study the numerical instability of advection upstream splitting method (AUSM) family schemes so called the AUSMD, AUSMV and AUSMDV schemes in two-dimensional structured triangular grids by examining the shock-induced anomalies produced by these original schemes in different test cases. A multidimensional dissipation technique is proposed for these schemes. The evolution of perturbations is also studied by means of a linearized discrete analysis to the odd–even decoupling problem. The recursive equations show that the AUSMDV-family schemes with the dissipation technique are less sensitive to these anomalies than the original schemes. Finally, the dissipation technique is extended to the second-order schemes and tested by several test cases.

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41

Li, Qin, Dong Sun, and Pengxin Liu. "Further Study on Errors in Metric Evaluation by Linear Upwind Schemes with Flux Splitting in Stationary Grids." Communications in Computational Physics 22, no. 1 (May 3, 2017): 64–94. http://dx.doi.org/10.4208/cicp.oa-2016-0123.

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AbstractThe importance of eliminating errors in grid-metric evaluation for high-order difference schemes has been widely recognized in recent years, and it is known from the proof by Vinokur and Yee (NASA TM 209598, 2000) that when conservative derivations of grid metric are used by Thomas, Lombard and Neier (AIAA J., 1978, 17(10) and J. Spacecraft and rocket, 1990, 27(2)), errors caused by metric evaluation could be eliminated by linear schemes when flux splitting is not considered. According to the above achievement, central schemes without the use of flux splitting could fulfill the requirement of error elimination. Difficulties will arise for upwind schemes to attain the objective when the splitting is considered. In this study, further investigations are made on three aspects: Firstly, an idea of central scheme decomposition is introduced, and the procedure to derive the central scheme is proposed to evaluate grid metrics only. Secondly, the analysis has been made on the requirement of flux splitting to acquire free-stream preservation, and a Lax-Friedrichs-type splitting scheme is proposed as an example. Discussions about current study with that by Nonomura et al. (Computers and Fluids, 2015, 107) have been made. Thirdly, for half-node- or mixed-type schemes, interpolations should be used to derive variables at half nodes. The requirement to achieve metric identity on this situation is analyzed and an idea of directionally consistent interpolation is proposed, which is manifested to be indispensable to avoid violations of metric identity and to eliminate metric-caused errors thereafter. Two numerical problems are tested, i.e., the free-stream and vortex preservation on wavy, largely randomized and triangular-like grids. Numerical results validate aforementioned theoretical outcomes.

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Beno, Matej, and Bořek Patzák. "FICTITIOUS DOMAIN METHOD FOR NUMERICAL SIMULATION OF INCOMPRESSIBLE VISCOUS FLOW AROUND RIGID BODIES." Acta Polytechnica 57, no. 4 (September 1, 2017): 245. http://dx.doi.org/10.14311/ap.2017.57.0245.

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This article describes the method of efficient simulation of the flow around potentially many rigid obstacles. The finite element implementation is based on the incompressible Navier-Stokes equations using structured, regular, two dimensional triangular mesh. The fictitious domain method is introduced to account for the presence of rigid particles, representing obstacles to the flow. To enforce rigid body constraints in parts corresponding to rigid obstacles, Lagrange multipliers are used. For time discretization, an operator splitting technique is used. The model is validated using 2D channel flow simulations with circular obstacles. Different possibilities of enforcing rigid body constraints are compared to the fully resolved simulations and optimal strategy is recommended.

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43

Dou, Yan, Ai-Li Yang, and Yu-Jiang Wu. "On semi-convergence of generalized skew-Hermitian triangular splitting iteration methods for singular saddle-point problems." Linear Algebra and its Applications 459 (October 2014): 493–510. http://dx.doi.org/10.1016/j.laa.2014.07.014.

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Krukier, Lev A., Tatiana S. Martynova, and Zhong-Zhi Bai. "Product-type skew-Hermitian triangular splitting iteration methods for strongly non-Hermitian positive definite linear systems." Journal of Computational and Applied Mathematics 232, no. 1 (October 2009): 3–16. http://dx.doi.org/10.1016/j.cam.2008.10.033.

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Fan, Hongtao, Xinyun Zhu, Yajing Li, and Bing Zheng. "A variant of relaxed triangular splitting preconditioners for generalized saddle point problems from Navier–Stokes equations." Applied Mathematics and Computation 362 (December 2019): 124495. http://dx.doi.org/10.1016/j.amc.2019.06.009.

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Zhang, Guo-Feng, Li-Dan Liao, and Zhao-Zheng Liang. "On parameterized generalized skew-Hermitian triangular splitting iteration method for singular and nonsingular saddle point problems." Applied Mathematics and Computation 254 (March 2015): 340–59. http://dx.doi.org/10.1016/j.amc.2014.12.120.

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Liu, Zhen Wen, and Chuan Bo Hao. "Apply Roof-Broken the Blasting Technique to Control Rock Burst." Applied Mechanics and Materials 522-524 (February 2014): 1377–81. http://dx.doi.org/10.4028/www.scientific.net/amm.522-524.1377.

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In working mining process of No.108 coal seam in Shengli Mine, the lower triangular goaf area hanging arch caused shock pressure. For this, The theoretical analysis do this weaken the roof through the roof-broken blasting technology, to optimize blasting design parameters, combined with the actual situation of the working surface to improve the blasting process, improve the top relief solve risk technology and solve the problem of rock burst. The application shows: successful implementation of advanced deep hole pre-splitting blasting to address a key challenge for charge and blasting technology, effective control of the roof power mutation occurs, improve the safety factor of the mining area, and provides an important mining work under similar conditions.

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Hu, Chenxuan, Haoming Zhang, Chen Jiang, and Hanbin Ma. "A geometrical model of pinch-off in digital microfluidics underpins “one-to-three” droplet generation." Applied Physics Letters 120, no. 12 (March 21, 2022): 121602. http://dx.doi.org/10.1063/5.0086953.

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Droplet generation is a fundamental sample handling procedure in digital microfluidics. In this work, a symmetric “one-to-three” droplet generation strategy is reported. A triangular model based on the geometrical relationship of reservoir droplets, sub-droplets, and liquid necks is proposed. Numerical investigation and corresponding experiments are performed. The results indicate that the proposed strategy produces a greater pressure difference for sub-droplet generation, especially when traditional droplet splitting is not possible with restricted microfluidics device geometries. The proposed geometrical model is a powerful tool to propose several improved droplet generation strategies. The “one-to-three” droplet generation strategy shows potential in practical applications and further studies for digital microfluidics platform.

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BÁRÁNY, BALÁZS. "On the Ledrappier–Young formula for self-affine measures." Mathematical Proceedings of the Cambridge Philosophical Society 159, no. 3 (August 3, 2015): 405–32. http://dx.doi.org/10.1017/s0305004115000419.

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AbstractLedrappier and Young introduced a relation between entropy, Lyapunov exponents and dimension for invariant measures of diffeomorphisms on compact manifolds. In this paper, we show that a self-affine measure on the plane satisfies the Ledrappier–Young formula if the corresponding iterated function system (IFS) satisfies the strong separation condition and the linear parts satisfy the dominated splitting condition. We give sufficient conditions, inspired by Ledrappier and by Falconer and Kempton, that the dimensions of such a self-affine measure is equal to the Lyapunov dimension. We show some applications, namely, we give another proof for Hueter–Lalley's theorem and we consider self-affine measures and sets generated by lower triangular matrices.

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Liu, Hongbao, Rong Huang, Wenxia Chen, Yiwei Zhang, Mengmeng Wang, Yingjie Hu, Yuming Zhou, and Youchao Song. "Porous 2D cobalt–nickel phosphide triangular nanowall architecture assembled by 3D microsphere for enhanced overall water splitting." Applied Surface Science 569 (December 2021): 150762. http://dx.doi.org/10.1016/j.apsusc.2021.150762.

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