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Meshfree methods (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Meshfree methods" in English language version.

refsWebsite
Global rank English rank
33doi.org
2nd place
2nd place
17harvard.edu
18th place
17th place
13semanticscholar.org
11th place
8th place
2nih.gov
4th place
4th place
1unt.edu
1,336th place
769th place
1ucla.edu
782nd place
585th place
1worldcat.org
5th place
5th place

doi.org

  • Gingold, R. A.; Monaghan, J. J. (1 December 1977). "Smoothed particle hydrodynamics: theory and application to non-spherical stars". Monthly Notices of the Royal Astronomical Society. 181 (3): 375–389. Bibcode:1977MNRAS.181..375G. doi:10.1093/mnras/181.3.375.
  • Libersky, Larry D.; Petschek, Albert G.; Carney, Theodore C.; Hipp, Jim R.; Allahdadi, Firooz A. (November 1993). "High Strain Lagrangian Hydrodynamics". Journal of Computational Physics. 109 (1): 67–75. doi:10.1006/jcph.1993.1199.
  • Swegle, J.W.; Hicks, D.L.; Attaway, S.W. (January 1995). "Smoothed Particle Hydrodynamics Stability Analysis". Journal of Computational Physics. 116 (1): 123–134. Bibcode:1995JCoPh.116..123S. doi:10.1006/jcph.1995.1010.
  • Nayroles, B.; Touzot, G.; Villon, P. (1992). "Generalizing the finite element method: Diffuse approximation and diffuse elements". Computational Mechanics. 10 (5): 307–318. Bibcode:1992CompM..10..307N. doi:10.1007/BF00364252. S2CID 121511161.
  • Belytschko, T.; Lu, Y. Y.; Gu, L. (30 January 1994). "Element-free Galerkin methods". International Journal for Numerical Methods in Engineering. 37 (2): 229–256. Bibcode:1994IJNME..37..229B. doi:10.1002/nme.1620370205.
  • Liu, Wing Kam; Jun, Sukky; Zhang, Yi Fei (30 April 1995). "Reproducing kernel particle methods". International Journal for Numerical Methods in Fluids. 20 (8–9): 1081–1106. Bibcode:1995IJNMF..20.1081L. doi:10.1002/fld.1650200824.
  • Sulsky, D.; Chen, Z.; Schreyer, H.L. (September 1994). "A particle method for history-dependent materials". Computer Methods in Applied Mechanics and Engineering. 118 (1–2): 179–196. doi:10.1016/0045-7825(94)90112-0.
  • Liu, W. K.; Chen, Y.; Jun, S.; Chen, J. S.; Belytschko, T.; Pan, C.; Uras, R. A.; Chang, C. T. (March 1996). "Overview and applications of the reproducing Kernel Particle methods". Archives of Computational Methods in Engineering. 3 (1): 3–80. doi:10.1007/BF02736130. S2CID 122241092.
  • Atluri, S. N.; Zhu, T. (24 August 1998). "A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics". Computational Mechanics. 22 (2): 117–127. Bibcode:1998CompM..22..117A. doi:10.1007/s004660050346. S2CID 3688083.
  • Oliveira, T.; Portela, A. (December 2016). "Weak-form collocation – A local meshless method in linear elasticity". Engineering Analysis with Boundary Elements. 73: 144–160. doi:10.1016/j.enganabound.2016.09.010.
  • Chen, Shang-Ying; Hsu, Kuo-Chin; Fan, Chia-Ming (15 March 2021). "Improvement of generalized finite difference method for stochastic subsurface flow modeling". Journal of Computational Physics. 429: 110002. Bibcode:2021JCoPh.42910002C. doi:10.1016/J.JCP.2020.110002. S2CID 228828681.
  • Chen, Shang-Ying; Wei, Jian-Yu; Hsu, Kuo-Chin (2023-10-01). "Data assimilation for real-time subsurface flow modeling with dynamically adaptive meshless node adjustments". Engineering with Computers. 40 (3): 1893–1925. doi:10.1007/s00366-023-01897-6. ISSN 1435-5663.
  • W.K. Liu; S. Jun; Y.F. Zhang (1995). "Reproducing kernel particle methods". Int. J. Numer. Methods Eng. 20 (8–9): 1081–1106. Bibcode:1995IJNMF..20.1081L. doi:10.1002/fld.1650200824.
  • A. Behzadan; H. M. Shodja; M. Khezri (2011). "A unified approach to the mathematical analysis of generalized RKPM, gradient RKPM, and GMLS". Comput. Methods. Appl. Mech. Eng. 200 (5–8): 540–576. Bibcode:2011CMAME.200..540B. doi:10.1016/j.cma.2010.07.017.
  • Gauger, Christoph; Leinen, Peter; Yserentant, Harry (January 2000). "The Finite Mass Method". SIAM Journal on Numerical Analysis. 37 (6): 1768–1799. doi:10.1137/S0036142999352564.
  • Li, B.; Habbal, F.; Ortiz, M. (17 September 2010). "Optimal transportation meshfree approximation schemes for fluid and plastic flows". International Journal for Numerical Methods in Engineering. 83 (12): 1541–1579. Bibcode:2010IJNME..83.1541L. doi:10.1002/nme.2869. S2CID 18225521.
  • Walker, Wade A.; Langowski, Jörg (6 July 2012). "The Repeated Replacement Method: A Pure Lagrangian Meshfree Method for Computational Fluid Dynamics". PLOS ONE. 7 (7): e39999. Bibcode:2012PLoSO...739999W. doi:10.1371/journal.pone.0039999. PMC 3391243. PMID 22866175.
  • Ooi, E.H.; Popov, V. (May 2012). "An efficient implementation of the radial basis integral equation method". Engineering Analysis with Boundary Elements. 36 (5): 716–726. doi:10.1016/j.enganabound.2011.12.001. S2CID 122004658.
  • Zhang, Xiong; Liu, Xiao-Hu; Song, Kang-Zu; Lu, Ming-Wan (30 July 2001). "Least-squares collocation meshless method". International Journal for Numerical Methods in Engineering. 51 (9): 1089–1100. Bibcode:2001IJNME..51.1089Z. doi:10.1002/nme.200. S2CID 119952479.
  • Boroomand, B.; Soghrati, S.; Movahedian, B. (2009). "Exponential basis functions in solution of static and time harmonic elastic problems in a meshless style". International Journal for Numerical Methods in Engineering. 81 (8): 971–1018. doi:10.1002/nme.2718. S2CID 4943418.
  • Chen, S.-Y.; Hsu, K.-C. (2024). "An efficient approach of meshless node placement in three-dimensional subsurface flow modeling". Engineering Analysis with Boundary Elements. 169(A): 105997. doi:10.1016/j.enganabound.2024.105997.
  • Ghoneim, A. (March 2015). "A meshfree interface-finite element method for modelling isothermal solutal melting and solidification in binary systems". Finite Elements in Analysis and Design. 95: 20–41. doi:10.1016/j.finel.2014.10.002.
  • Chen, Jiun-Shyan; Hillman, Michael; Chi, Sheng-Wei (April 2017). "Meshfree Methods: Progress Made after 20 Years". Journal of Engineering Mechanics. 143 (4): 04017001. doi:10.1061/(ASCE)EM.1943-7889.0001176.
  • Belytschko, Ted; Guo, Yong; Kam Liu, Wing; Ping Xiao, Shao (30 July 2000). "A unified stability analysis of meshless particle methods". International Journal for Numerical Methods in Engineering. 48 (9): 1359–1400. Bibcode:2000IJNME..48.1359B. doi:10.1002/1097-0207(20000730)48:9<1359::AID-NME829>3.0.CO;2-U.
  • Chen, Jiun-Shyan; Wu, Cheng-Tang; Yoon, Sangpil; You, Yang (20 January 2001). "A stabilized conforming nodal integration for Galerkin mesh-free methods". International Journal for Numerical Methods in Engineering. 50 (2): 435–466. Bibcode:2001IJNME..50..435C. doi:10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A.
  • Chen, Jiun-Shyan; Hillman, Michael; Rüter, Marcus (3 August 2013). "An arbitrary order variationally consistent integration for Galerkin meshfree methods". International Journal for Numerical Methods in Engineering. 95 (5): 387–418. Bibcode:2013IJNME..95..387C. doi:10.1002/nme.4512. S2CID 124640562.
  • Liu, G. R. (2009). "A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part I theory". International Journal for Numerical Methods in Engineering. 81 (9): 1093–1126. doi:10.1002/nme.2719. S2CID 123009384.
  • Liu, G. R. (2009). "A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part II applications to solid mechanics problems". International Journal for Numerical Methods in Engineering. 81 (9): 1127–1156. doi:10.1002/nme.2720. S2CID 119378545.
  • Liu, G. R.; Zhang, G. Y. (20 November 2011). "A normed G space and weakened weak (W2) formulation of a cell-based smoothed point interpolation method". International Journal of Computational Methods. 06 (1): 147–179. doi:10.1142/S0219876209001796.
  • Liu, G. R.; Zhang, G. Y. (14 May 2008). "Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC-PIM)". International Journal for Numerical Methods in Engineering. 74 (7): 1128–1161. Bibcode:2008IJNME..74.1128L. doi:10.1002/nme.2204. S2CID 54088894.
  • Liu, G. R.; Xu, George X. (10 December 2008). "A gradient smoothing method (GSM) for fluid dynamics problems". International Journal for Numerical Methods in Fluids. 58 (10): 1101–1133. Bibcode:2008IJNMF..58.1101L. doi:10.1002/fld.1788. S2CID 53983110.
  • Zhang, Jian; Liu, G.R.; Lam, K.Y.; Li, Hua; Xu, G. (November 2008). "A gradient smoothing method (GSM) based on strong form governing equation for adaptive analysis of solid mechanics problems". Finite Elements in Analysis and Design. 44 (15): 889–909. doi:10.1016/j.finel.2008.06.006.
  • Liu, G. R. (20 November 2011). "On G space theory". International Journal of Computational Methods. 06 (2): 257–289. doi:10.1142/S0219876209001863.

harvard.edu

ui.adsabs.harvard.edu

  • Gingold, R. A.; Monaghan, J. J. (1 December 1977). "Smoothed particle hydrodynamics: theory and application to non-spherical stars". Monthly Notices of the Royal Astronomical Society. 181 (3): 375–389. Bibcode:1977MNRAS.181..375G. doi:10.1093/mnras/181.3.375.
  • Swegle, J.W.; Hicks, D.L.; Attaway, S.W. (January 1995). "Smoothed Particle Hydrodynamics Stability Analysis". Journal of Computational Physics. 116 (1): 123–134. Bibcode:1995JCoPh.116..123S. doi:10.1006/jcph.1995.1010.
  • Nayroles, B.; Touzot, G.; Villon, P. (1992). "Generalizing the finite element method: Diffuse approximation and diffuse elements". Computational Mechanics. 10 (5): 307–318. Bibcode:1992CompM..10..307N. doi:10.1007/BF00364252. S2CID 121511161.
  • Belytschko, T.; Lu, Y. Y.; Gu, L. (30 January 1994). "Element-free Galerkin methods". International Journal for Numerical Methods in Engineering. 37 (2): 229–256. Bibcode:1994IJNME..37..229B. doi:10.1002/nme.1620370205.
  • Liu, Wing Kam; Jun, Sukky; Zhang, Yi Fei (30 April 1995). "Reproducing kernel particle methods". International Journal for Numerical Methods in Fluids. 20 (8–9): 1081–1106. Bibcode:1995IJNMF..20.1081L. doi:10.1002/fld.1650200824.
  • Atluri, S. N.; Zhu, T. (24 August 1998). "A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics". Computational Mechanics. 22 (2): 117–127. Bibcode:1998CompM..22..117A. doi:10.1007/s004660050346. S2CID 3688083.
  • Chen, Shang-Ying; Hsu, Kuo-Chin; Fan, Chia-Ming (15 March 2021). "Improvement of generalized finite difference method for stochastic subsurface flow modeling". Journal of Computational Physics. 429: 110002. Bibcode:2021JCoPh.42910002C. doi:10.1016/J.JCP.2020.110002. S2CID 228828681.
  • W.K. Liu; S. Jun; Y.F. Zhang (1995). "Reproducing kernel particle methods". Int. J. Numer. Methods Eng. 20 (8–9): 1081–1106. Bibcode:1995IJNMF..20.1081L. doi:10.1002/fld.1650200824.
  • A. Behzadan; H. M. Shodja; M. Khezri (2011). "A unified approach to the mathematical analysis of generalized RKPM, gradient RKPM, and GMLS". Comput. Methods. Appl. Mech. Eng. 200 (5–8): 540–576. Bibcode:2011CMAME.200..540B. doi:10.1016/j.cma.2010.07.017.
  • Li, B.; Habbal, F.; Ortiz, M. (17 September 2010). "Optimal transportation meshfree approximation schemes for fluid and plastic flows". International Journal for Numerical Methods in Engineering. 83 (12): 1541–1579. Bibcode:2010IJNME..83.1541L. doi:10.1002/nme.2869. S2CID 18225521.
  • Walker, Wade A.; Langowski, Jörg (6 July 2012). "The Repeated Replacement Method: A Pure Lagrangian Meshfree Method for Computational Fluid Dynamics". PLOS ONE. 7 (7): e39999. Bibcode:2012PLoSO...739999W. doi:10.1371/journal.pone.0039999. PMC 3391243. PMID 22866175.
  • Zhang, Xiong; Liu, Xiao-Hu; Song, Kang-Zu; Lu, Ming-Wan (30 July 2001). "Least-squares collocation meshless method". International Journal for Numerical Methods in Engineering. 51 (9): 1089–1100. Bibcode:2001IJNME..51.1089Z. doi:10.1002/nme.200. S2CID 119952479.
  • Belytschko, Ted; Guo, Yong; Kam Liu, Wing; Ping Xiao, Shao (30 July 2000). "A unified stability analysis of meshless particle methods". International Journal for Numerical Methods in Engineering. 48 (9): 1359–1400. Bibcode:2000IJNME..48.1359B. doi:10.1002/1097-0207(20000730)48:9<1359::AID-NME829>3.0.CO;2-U.
  • Chen, Jiun-Shyan; Wu, Cheng-Tang; Yoon, Sangpil; You, Yang (20 January 2001). "A stabilized conforming nodal integration for Galerkin mesh-free methods". International Journal for Numerical Methods in Engineering. 50 (2): 435–466. Bibcode:2001IJNME..50..435C. doi:10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A.
  • Chen, Jiun-Shyan; Hillman, Michael; Rüter, Marcus (3 August 2013). "An arbitrary order variationally consistent integration for Galerkin meshfree methods". International Journal for Numerical Methods in Engineering. 95 (5): 387–418. Bibcode:2013IJNME..95..387C. doi:10.1002/nme.4512. S2CID 124640562.
  • Liu, G. R.; Zhang, G. Y. (14 May 2008). "Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC-PIM)". International Journal for Numerical Methods in Engineering. 74 (7): 1128–1161. Bibcode:2008IJNME..74.1128L. doi:10.1002/nme.2204. S2CID 54088894.
  • Liu, G. R.; Xu, George X. (10 December 2008). "A gradient smoothing method (GSM) for fluid dynamics problems". International Journal for Numerical Methods in Fluids. 58 (10): 1101–1133. Bibcode:2008IJNMF..58.1101L. doi:10.1002/fld.1788. S2CID 53983110.

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  • Nayroles, B.; Touzot, G.; Villon, P. (1992). "Generalizing the finite element method: Diffuse approximation and diffuse elements". Computational Mechanics. 10 (5): 307–318. Bibcode:1992CompM..10..307N. doi:10.1007/BF00364252. S2CID 121511161.
  • Liu, W. K.; Chen, Y.; Jun, S.; Chen, J. S.; Belytschko, T.; Pan, C.; Uras, R. A.; Chang, C. T. (March 1996). "Overview and applications of the reproducing Kernel Particle methods". Archives of Computational Methods in Engineering. 3 (1): 3–80. doi:10.1007/BF02736130. S2CID 122241092.
  • Atluri, S. N.; Zhu, T. (24 August 1998). "A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics". Computational Mechanics. 22 (2): 117–127. Bibcode:1998CompM..22..117A. doi:10.1007/s004660050346. S2CID 3688083.
  • Chen, Shang-Ying; Hsu, Kuo-Chin; Fan, Chia-Ming (15 March 2021). "Improvement of generalized finite difference method for stochastic subsurface flow modeling". Journal of Computational Physics. 429: 110002. Bibcode:2021JCoPh.42910002C. doi:10.1016/J.JCP.2020.110002. S2CID 228828681.
  • Li, B.; Habbal, F.; Ortiz, M. (17 September 2010). "Optimal transportation meshfree approximation schemes for fluid and plastic flows". International Journal for Numerical Methods in Engineering. 83 (12): 1541–1579. Bibcode:2010IJNME..83.1541L. doi:10.1002/nme.2869. S2CID 18225521.
  • Ooi, E.H.; Popov, V. (May 2012). "An efficient implementation of the radial basis integral equation method". Engineering Analysis with Boundary Elements. 36 (5): 716–726. doi:10.1016/j.enganabound.2011.12.001. S2CID 122004658.
  • Zhang, Xiong; Liu, Xiao-Hu; Song, Kang-Zu; Lu, Ming-Wan (30 July 2001). "Least-squares collocation meshless method". International Journal for Numerical Methods in Engineering. 51 (9): 1089–1100. Bibcode:2001IJNME..51.1089Z. doi:10.1002/nme.200. S2CID 119952479.
  • Boroomand, B.; Soghrati, S.; Movahedian, B. (2009). "Exponential basis functions in solution of static and time harmonic elastic problems in a meshless style". International Journal for Numerical Methods in Engineering. 81 (8): 971–1018. doi:10.1002/nme.2718. S2CID 4943418.
  • Chen, Jiun-Shyan; Hillman, Michael; Rüter, Marcus (3 August 2013). "An arbitrary order variationally consistent integration for Galerkin meshfree methods". International Journal for Numerical Methods in Engineering. 95 (5): 387–418. Bibcode:2013IJNME..95..387C. doi:10.1002/nme.4512. S2CID 124640562.
  • Liu, G. R. (2009). "A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part I theory". International Journal for Numerical Methods in Engineering. 81 (9): 1093–1126. doi:10.1002/nme.2719. S2CID 123009384.
  • Liu, G. R. (2009). "A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part II applications to solid mechanics problems". International Journal for Numerical Methods in Engineering. 81 (9): 1127–1156. doi:10.1002/nme.2720. S2CID 119378545.
  • Liu, G. R.; Zhang, G. Y. (14 May 2008). "Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC-PIM)". International Journal for Numerical Methods in Engineering. 74 (7): 1128–1161. Bibcode:2008IJNME..74.1128L. doi:10.1002/nme.2204. S2CID 54088894.
  • Liu, G. R.; Xu, George X. (10 December 2008). "A gradient smoothing method (GSM) for fluid dynamics problems". International Journal for Numerical Methods in Fluids. 58 (10): 1101–1133. Bibcode:2008IJNMF..58.1101L. doi:10.1002/fld.1788. S2CID 53983110.

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