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1

Monaghan, J. J. "Smoothed Particle Hydrodynamics." Annual Review of Astronomy and Astrophysics 30, no. 1 (1992): 543–74. http://dx.doi.org/10.1146/annurev.aa.30.090192.002551.

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2

Monaghan, J. J. "Smoothed particle hydrodynamics." Reports on Progress in Physics 68, no. 8 (2005): 1703–59. http://dx.doi.org/10.1088/0034-4885/68/8/r01.

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3

Umemura, Masayuki, Toshiyuki Fukushige, Junichiro Makino, et al. "Smoothed Particle Hydrodynamics with GRAPE-1A." Publications of the Astronomical Society of Japan 45, no. 3 (1993): 311–20. https://doi.org/10.1093/pasj/45.3.311.

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Abstract We describe the implementation of a smoothed particle hydrodynamics (SPH) scheme using GRAPElA, a special-purpose processor used for gravitational N-body simulations. The GRAPE-1A calculates the gravitational force exerted on a particle from all other particles in a system, while simultaneously making a list of the nearest neighbors of the particle. If a host computer, which is connected to GRAPE-1A, uses this neighbor list in order to calculate hydrodynamical variables, the computational cost of SPH can be greatly reduced. It is found that GRAPE-1A accelerates SPH calculations by dir
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4

Li, Hongbin, Lixuan Zhang, Zhongxiang Shen, and Wenqing Wang. "Cone structure‒ice interaction simulation based on the common-node discrete element method–smoothed particle hydrodynamics coupling method." Advances in Engineering Technology Research 11, no. 1 (2024): 846. http://dx.doi.org/10.56028/aetr.11.1.846.2024.

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This paper presents a novel approach utilizing the discrete element method (DEM) and smoothed particle hydrodynamics (SPH). A new fluid–structure coupling method called the common-node discrete element method–smoothed particle hydrodynamics (DS–SPH) is proposed. The DS-SPH method involves establishing a DEM and SPH method on the same node to create common-node discrete element-smoothed particle hydrodynamics (DEM-SPH, DS) particles. This enables the DEM particles to experience forces exerted by the SPH particles within their supporting region through the SPH particles located at the same node.
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5

Ritchie, B. W., and P. A. Thomas. "Multiphase smoothed-particle hydrodynamics." Monthly Notices of the Royal Astronomical Society 323, no. 3 (2001): 743–56. http://dx.doi.org/10.1046/j.1365-8711.2001.04268.x.

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6

Cullen, Lee, and Walter Dehnen. "Inviscid smoothed particle hydrodynamics." Monthly Notices of the Royal Astronomical Society 408, no. 2 (2010): 669–83. http://dx.doi.org/10.1111/j.1365-2966.2010.17158.x.

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7

Tsuji, P., M. Puso, C. W. Spangler, J. M. Owen, D. Goto, and T. Orzechowski. "Embedded smoothed particle hydrodynamics." Computer Methods in Applied Mechanics and Engineering 366 (July 2020): 113003. http://dx.doi.org/10.1016/j.cma.2020.113003.

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8

Ellero, Marco, Mar Serrano, and Pep Español. "Incompressible smoothed particle hydrodynamics." Journal of Computational Physics 226, no. 2 (2007): 1731–52. http://dx.doi.org/10.1016/j.jcp.2007.06.019.

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9

Petschek, A. G., and L. D. Libersky. "Cylindrical Smoothed Particle Hydrodynamics." Journal of Computational Physics 109, no. 1 (1993): 76–83. http://dx.doi.org/10.1006/jcph.1993.1200.

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10

Tavakkol, Sasan, Amir Reza Zarrati, and Mahdiyar Khanpour. "Curvilinear smoothed particle hydrodynamics." International Journal for Numerical Methods in Fluids 83, no. 2 (2016): 115–31. http://dx.doi.org/10.1002/fld.4261.

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11

Wang, Jingsi, Shaolin Xu, Keita Shimada, Masayoshi Mizutani, and Tsunemoto Kuriyagawa. "Smoothed particle hydrodynamics simulation and experimental study of ultrasonic machining." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 232, no. 11 (2017): 1875–84. http://dx.doi.org/10.1177/0954405417692005.

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Hard and brittle materials like glass and ceramics are highly demanded in modern manufacturing industries. However, their superior physical and mechanical properties lead to high cost of machining. Ultrasonic machining has been regarded as one of the most suitable fabrication techniques for these kinds of materials. A smoothed particle hydrodynamics model was proposed to study the material removal mechanism of the ultrasonic machining in this study. Influences of abrasive materials and the particle shapes on the crack formation of work substrates were investigated using this smoothed particle
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12

Trimulyono, Andi. "Validasi Gerakan Benda Terapung Menggunakan Metode Smoothed Particle Hydrodynamics." Kapal: Jurnal Ilmu Pengetahuan dan Teknologi Kelautan 15, no. 2 (2018): 38–43. http://dx.doi.org/10.14710/kpl.v15i2.17802.

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13

Hedayati, Ehsan, and Mohammad Vahedi. "Evaluating Impact Resistance of Aluminum 6061-T651 Plate using Smoothed Particle Hydrodynamics Method." Defence Science Journal 68, no. 3 (2018): 251. http://dx.doi.org/10.14429/dsj.68.11635.

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Performing various experimental, theoretical, and numerical investigations for better understanding of behavioural characteristics of metals under impact loading is of primary importance. In this paper, application of smoothed particle hydrodynamics (SPH) method in impact mechanics is discussed and effective parameters on impact strength of an aluminum plate are investigated. To evaluate the accuracy of smoothed particle hydrodynamics method for simulating impact, Recht and Ipson model is first provided thoroughly for both Rosenberg analytical model and smoothed particle hydrodynamics method,
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14

Murante, G., S. Borgani, R. Brunino, and S. H. Cha. "Hydrodynamic simulations with the Godunov smoothed particle hydrodynamics." Monthly Notices of the Royal Astronomical Society 417, no. 1 (2011): 136–53. http://dx.doi.org/10.1111/j.1365-2966.2011.19021.x.

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15

Yamamoto, Satoko, Takayuki R. Saitoh, and Junichiro Makino. "Smoothed particle hydrodynamics with smoothed pseudo-density." Publications of the Astronomical Society of Japan 67, no. 3 (2015): 37. http://dx.doi.org/10.1093/pasj/psv006.

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16

Su, Chong, Li Da Zhu, and Wan Shan Wang. "Simulation Research on Cutting Process of Single Abrasive Grain." Advanced Materials Research 239-242 (May 2011): 3123–26. http://dx.doi.org/10.4028/www.scientific.net/amr.239-242.3123.

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Cutting processes of single abrasive grain were simulated respectively by fluid-solid interaction method and Smoothed Particle Hydrodynamics method. Advantages and disadvantages of the two methods were compared. Smoothed Particle Hydrodynamics method is superior to fluid-solid interaction method in simulating the deformation behavior of workpiece material for the motion of SPH particles. According to the simulation results, it is concluded that workpiece material occurs plastic deformation, flows to the side and front owing to the extrusion of abrasive grain, and finally forms chip in front of
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17

Muhammad Haseeb, Hasan Aftab Saeed, and Imran Sajid S. Ghumman. "Numerical Simulation of Orthogonal Machining of Gallium Nitride via Smoothed Particle Hydrodynamics." NUML International Journal of Engineering and Computing 1, no. 1 (2022): 27–38. http://dx.doi.org/10.52015/nijec.v1i1.11.

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Gallium Nitride is one of the best candidates for upcoming industrial revolution due to itssuperior electrical properties over silicon. In the present work, we investigate the chipformation, cutting force and effective stress in diamond machining of gallium nitride bysmoothed particle hydrodynamics approach based on Mohr-Coulomb material model. Thecomparison of the effective stress as reported by molecular dynamics studies and thatpredicted by the smoothed particle hydrodynamics simulation demonstrates the effectivenessof the smoothed particle hydrodynamics model.
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18

Liptai, David, and Daniel J. Price. "General relativistic smoothed particle hydrodynamics." Monthly Notices of the Royal Astronomical Society 485, no. 1 (2019): 819–42. http://dx.doi.org/10.1093/mnras/stz111.

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19

Springel, Volker. "Smoothed Particle Hydrodynamics in Astrophysics." Annual Review of Astronomy and Astrophysics 48, no. 1 (2010): 391–430. http://dx.doi.org/10.1146/annurev-astro-081309-130914.

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20

Monaghan, Joseph J., Herbert E. Huppert, and M. Grae Worster. "Solidification using smoothed particle hydrodynamics." Journal of Computational Physics 206, no. 2 (2005): 684–705. http://dx.doi.org/10.1016/j.jcp.2004.11.039.

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21

Ayal, S., T. Piran, R. Oechslin, M. B. Davies, and S. Rosswog. "Post‐Newtonian Smoothed Particle Hydrodynamics." Astrophysical Journal 550, no. 2 (2001): 846–59. http://dx.doi.org/10.1086/319769.

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22

Wong, S., and Y. Shie. "Galerkin based smoothed particle hydrodynamics." Computers & Structures 87, no. 17-18 (2009): 1111–18. http://dx.doi.org/10.1016/j.compstruc.2009.04.010.

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23

Price, Daniel J. "Smoothed particle hydrodynamics and magnetohydrodynamics." Journal of Computational Physics 231, no. 3 (2012): 759–94. http://dx.doi.org/10.1016/j.jcp.2010.12.011.

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24

Swegle, J. W., D. L. Hicks, and S. W. Attaway. "Smoothed Particle Hydrodynamics Stability Analysis." Journal of Computational Physics 116, no. 1 (1995): 123–34. http://dx.doi.org/10.1006/jcph.1995.1010.

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25

Trimulyono, Andi, and Ardhana Wicaksono. "Simulasi numerik large-deformation surface wave dengan smoothed particle hydrodynamics." Kapal: Jurnal Ilmu Pengetahuan dan Teknologi Kelautan 15, no. 3 (2019): 102–6. http://dx.doi.org/10.14710/kapal.v15i3.21535.

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26

Wang, Sheng, Yong Ou Zhang, and Jing Ping Wu. "Lagrangian meshfree finite difference particle method with variable smoothing length for solving wave equations." Advances in Mechanical Engineering 10, no. 7 (2018): 168781401878924. http://dx.doi.org/10.1177/1687814018789248.

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In a Lagrangian meshfree particle-based method, the smoothing length determines the size of the support domain for each particle. Since the particle distribution is irregular and uneven in most cases, a fixed smoothing length sometime brings too much or insufficient neighbor particles for the weight function which reduces the numerical accuracy. In this work, a Lagrangian meshfree finite difference particle method with variable smoothing length is proposed for solving different wave equations. This pure Lagrangian method combines the generalized finite difference scheme for spatial resolution
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27

Liu, M. B., and G. R. Liu. "Restoring particle consistency in smoothed particle hydrodynamics." Applied Numerical Mathematics 56, no. 1 (2006): 19–36. http://dx.doi.org/10.1016/j.apnum.2005.02.012.

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28

Lastiwka, Martin, Nathan Quinlan, and Mihai Basa. "Adaptive particle distribution for smoothed particle hydrodynamics." International Journal for Numerical Methods in Fluids 47, no. 10-11 (2005): 1403–9. http://dx.doi.org/10.1002/fld.891.

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29

Dong, Xiangwei, Zengliang Li, Qi Zhang, Wei Zeng, and G. R. Liu. "Analysis of surface-erosion mechanism due to impacts of freely rotating angular particles using smoothed particle hydrodynamics erosion model." Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 231, no. 12 (2017): 1537–51. http://dx.doi.org/10.1177/1350650117700750.

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The free rotation of an angular particle during its impact on ductile surfaces is an important factor that influences the erosion mechanism. However, the phenomenon cannot be easily revealed experimentally because the incident conditions cannot be accurately controlled. In this study, a novel erosion model based on smoothed particle hydrodynamics method is proposed to simulate single and multiple impacts of particles with specified angularities on a ductile surface. The model can simulate a particle having free rotation during the impact process and initial rotation prior to the impact. The re
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30

LIU, M. B., G. R. LIU, and Z. ZONG. "AN OVERVIEW ON SMOOTHED PARTICLE HYDRODYNAMICS." International Journal of Computational Methods 05, no. 01 (2008): 135–88. http://dx.doi.org/10.1142/s021987620800142x.

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This paper presents an overview on smoothed particle hydrodynamics (SPH), which is a meshfree, particle method of Lagrangian nature. In theory, the interpolation and approximations of the SPH method and the corresponding numerical errors are analyzed. The inherent particle inconsistency has been discussed in detail. It has been demonstrated that the particle inconsistency originates from the discrete particle approximation process and is the fundamental cause for poor approximation accuracy. Some particle consistency restoring approaches have been reviewed. In application, SPH modeling of gene
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31

Daropoulos, Viktor, Matthias Augustin, and Joachim Weickert. "Sparse Inpainting with Smoothed Particle Hydrodynamics." SIAM Journal on Imaging Sciences 14, no. 4 (2021): 1669–705. http://dx.doi.org/10.1137/20m1382179.

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32

Wissing, Robert, Sijing Shen, James Wadsley, and Thomas Quinn. "Magnetorotational instability with smoothed particle hydrodynamics." Astronomy & Astrophysics 659 (March 2022): A91. http://dx.doi.org/10.1051/0004-6361/202141206.

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The magnetorotational instability (MRI) is an important process in driving turbulence in sufficiently ionized accretion disks. It has been extensively studied using simulations with Eulerian grid codes, but remains fairly unexplored for meshless codes. Here, we present a thorough numerical study on the MRI using the smoothed particle magnetohydrodynamics method with the geometric density average force expression. We performed 37 shearing box simulations with different initial setups and a wide range of resolution and dissipation parameters. We show, for the first time, that MRI with sustained
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33

Quinlan, Nathan J., and Mingming Tong. "Industrial Applications of Smoothed Particle Hydrodynamics." International Journal of Computational Fluid Dynamics 35, no. 1-2 (2021): 1–2. http://dx.doi.org/10.1080/10618562.2021.1946946.

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34

Wang, Mengdi, Yitong Deng, Xiangxin Kong, Aditya H. Prasad, Shiying Xiong, and Bo Zhu. "Thin-film smoothed particle hydrodynamics fluid." ACM Transactions on Graphics 40, no. 4 (2021): 1–16. http://dx.doi.org/10.1145/3476576.3476675.

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35

Wang, Mengdi, Yitong Deng, Xiangxin Kong, Aditya H. Prasad, Shiying Xiong, and Bo Zhu. "Thin-film smoothed particle hydrodynamics fluid." ACM Transactions on Graphics 40, no. 4 (2021): 1–16. http://dx.doi.org/10.1145/3450626.3459864.

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36

Kodama, T., C. E. Aguiar, T. Osada, and Y. Hama. "Entropy-based relativistic smoothed particle hydrodynamics." Journal of Physics G: Nuclear and Particle Physics 27, no. 3 (2001): 557–60. http://dx.doi.org/10.1088/0954-3899/27/3/336.

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37

Krištof, P., B. Beneš, J. Křivánek, and O. Št'ava. "Hydraulic Erosion Using Smoothed Particle Hydrodynamics." Computer Graphics Forum 28, no. 2 (2009): 219–28. http://dx.doi.org/10.1111/j.1467-8659.2009.01361.x.

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38

Oxley, S., and M. M. Woolfson. "Smoothed particle hydrodynamics with radiation transfer." Monthly Notices of the Royal Astronomical Society 343, no. 3 (2003): 900–912. http://dx.doi.org/10.1046/j.1365-8711.2003.06751.x.

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39

Kessel-Deynet, O., and A. Burkert. "Ionizing radiation in smoothed particle hydrodynamics." Monthly Notices of the Royal Astronomical Society 315, no. 4 (2000): 713–21. http://dx.doi.org/10.1046/j.1365-8711.2000.03451.x.

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40

Oger, L., and S. B. Savage. "Smoothed particle hydrodynamics for cohesive grains." Computer Methods in Applied Mechanics and Engineering 180, no. 1-2 (1999): 169–83. http://dx.doi.org/10.1016/s0045-7825(99)00054-7.

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41

Imaeda, Yusuke, and Shu‐ichiro Inutsuka. "Shear Flows in Smoothed Particle Hydrodynamics." Astrophysical Journal 569, no. 1 (2002): 501–18. http://dx.doi.org/10.1086/339320.

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42

Abadi, Mario G., Diego G. Lambas, and Patricia B. Tissera. "Cosmological Simulations with Smoothed Particle Hydrodynamics." Symposium - International Astronomical Union 168 (1996): 577–78. http://dx.doi.org/10.1017/s0074180900110757.

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We have developed and tested a code that computes the evolution of a mixed system of gas and dark matter in expanding world models. The gravitational forces are calculated with the Adaptative P3M algorithms developed by H. Couchmann, 1993. The calculation of gas forces follow the standard SPH formalism (Monaghan, 1989).
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43

Fulk, David A., and Dennis W. Quinn. "Hybrid Formulations of smoothed particle hydrodynamics." International Journal of Impact Engineering 17, no. 1-3 (1995): 329–40. http://dx.doi.org/10.1016/0734-743x(95)99859-p.

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44

Zhou, Dai, Si Chen, Lei Li, Huafeng Li, and Yaojun Zhao. "Accuracy Improvement of Smoothed Particle Hydrodynamics." Engineering Applications of Computational Fluid Mechanics 2, no. 2 (2008): 244–51. http://dx.doi.org/10.1080/19942060.2008.11015225.

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45

Owen, J. Michael, Jens V. Villumsen, Paul R. Shapiro, and Hugo Martel. "Adaptive Smoothed Particle Hydrodynamics: Methodology. II." Astrophysical Journal Supplement Series 116, no. 2 (1998): 155–209. http://dx.doi.org/10.1086/313100.

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46

OBARA, Haruki, Mariko HONDA, and Akinori KOYAMA. "Fundamental Study of Smoothed Particle Hydrodynamics." Journal of Computational Science and Technology 2, no. 1 (2008): 101–10. http://dx.doi.org/10.1299/jcst.2.101.

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47

OBARA, Haruki, Jhun SUEMURA, and Mariko HONDA. "Fundamental Study of Smoothed Particle Hydrodynamics." Journal of Computational Science and Technology 2, no. 1 (2008): 92–100. http://dx.doi.org/10.1299/jcst.2.92.

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48

Zhu, Qirong, Lars Hernquist, and Yuexing Li. "NUMERICAL CONVERGENCE IN SMOOTHED PARTICLE HYDRODYNAMICS." Astrophysical Journal 800, no. 1 (2015): 6. http://dx.doi.org/10.1088/0004-637x/800/1/6.

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49

Rosswog, Stephan. "Conservative, special-relativistic smoothed particle hydrodynamics." Journal of Computational Physics 229, no. 22 (2010): 8591–612. http://dx.doi.org/10.1016/j.jcp.2010.08.002.

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50

Liu, M. B., G. R. Liu, and Shaofan Li. "?Smoothed particle hydrodynamics ? a meshfree method?" Computational Mechanics 33, no. 6 (2004): 491. http://dx.doi.org/10.1007/s00466-004-0573-1.

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