A Text-Mining-Based Approach for Conducting Literature Review of Selected Meshfree Methods

S. Sindhusuta; Sheng-Wei Chi; Sybil Derrible

doi:10.24423/cames.382

S. Sindhusuta University of Illinois at Chicago
Sheng-Wei Chi University of Illinois at Chicago
Sybil Derrible University of Illinois at Chicago

DOI: http://dx.doi.org/10.24423/cames.382

Abstract

The goal of this study is to review the literature in the field of meshfree methods using text mining. For this study, the abstracts of around 17 330 relevant articles published from 1990 to 2020 were collected from Scopus. Text mining techniques such as the latent Dirichlet allocation (LDA), along with the calculation of term frequencies and co-occurrence coefficients were used to analyze the text. The study identified a few key topics in the field of meshfree methods and helped to see the evolution of the field over the past three decades. Furthermore, the trend in the number of publications and frequency map highlighted research trends and lack of focus in certain areas. The co-author network visualization provided interesting insights about collaboration between different researchers around the world. Overall, this study facilitates a systematic literature review in the field of meshfree methods and provides a broader perspective of the field to the research community.

Keywords

meshfree methods, text-mining, latent Dirichlet allocation, topic modeling, literature review,

References

1. L.B.Lucy,A numerical approach to the testing of the fission hypothesis, The Astronomical Journal, 82(12): 1013–1024, 1977.
2. T. Belytschko, Y.Y. Lu, L. Gu, Element-free Galerkin methods, International Journal for Numerical Methods in Engineering, 37(2): 229–256, 1994, doi: 10.1002/nme.1620370205.
3. Y.Y. Lu, T. Belytschko, L. Gu, A new implementation of the element free Galerkin method, Computer Methods in Applied Mechanics and Engineering, 113(3–4): 397–414, 1994 doi: 10.1016/0045-7825(94)90056-6.
4. T. Belytschko, Y.Y. Lu, L. Gu, Crack propagation by element-free Galerkin methods, Engineering Fracture Mechanics, 51(2): 295–315, 1995, doi: 10.1016/0013-7944(94)00153-9.
5. J.-S. Chen, C. Pan, C.-T. Wu, W.K. Liu, Reproducing kernel particle methods for large deformation analysis of non-linear structures, Computer Methods in Applied Mechanics and Engineering, 139(1–4): 195–227, 1996, doi: 10.1016/S0045-7825(96)01083-3.
6. J.S. Chen, C.-T. Wu, S. Yoon, Y. You, A stabilized conforming nodal integration for Galerkin meshfree methods, International Journal for Numerical Methods in Engineering, 50(2): 435–466, 2001, doi: 10.1002/1097-0207(20010120)50:2<435::AID- NME32>3.0.CO;2-A.
7. J.-S. Chen, M. Hillman, S.-W. Chi, Meshfree methods: progress made after 20 years, Journal of Engineering Mechanics, 143(4): 04017001, 2017, doi: 10.1061/(ASCE)EM.1943-7889.0001176.
8. S.A. Silling, E. Askari, A meshfree method based on the peridynamic model of solid mechanics, Computers & Structures, 83(17–18): 1526–1535, 2005, doi: 10.1016/j.compstruc.2004.11.026.
9. G.-R. Liu, Y.-T. Gu, An Introduction to Meshfree Methods and Their Programming, Springer Science & Business Media, Dordrecht, 2005.
10. O. Zienkiewicz, R. Taylor, The Finite Element Method, McGraw-Hill, New York, 1977.
11. G.E. Forsythe, W.R. Wasow, Finite Difference Methods for Partial Differential Equations, Wiley & Sons, New York, 1960.
12. W.K. Liu, S. Jun, Multiple-scale reproducing kernel particle methods for large deformation problems, International Journal for Numerical Methods in Engineering, 41(7): 1339–1362, 1998, doi: 10.1002/(SICI)1097-0207(19980415)41:7<1339::AID-NME343>3.0.CO;2-9.
13. S. Yoon, J.-S. Chen, Accelerated mesh free method for metal forming simulation, Finite Elements in Analysis and Design, 38(10): 937–948, 2002, doi: 10.1016/S0168-874X(02)00086-0.
14. J.-S. Chen, C. Pan, C.-T. Wu, Large deformation analysis of rubber based on a reproducing kernel particle method, Computational Mechanics, 19(3): 211–227, 1997, doi: 10.1007/ s004660050170.
15. T. Rabczuk, T. Belytschko, A three-dimensional large deformation meshfree method for arbitrary evolving cracks, Computer Methods in Applied Mechanics and Engineering, 196(29–30): 2777–2799, 2007, doi: 10.1016/j.cma.2006.06.020.
16. S.-W. Chi, Image-Based Computational Mechanics Frameworks for Skeletal Muscles, University of California, PhD Dissertation, ProQuest Dissertations Publishing, Los Angeles, 2009.
17. J.-S. Chen, R.R. Basava, Y. Zhang, R. Csapo, V. Malis, U. Sinha, J. Hodgson, S. Sinha, Pixel-based meshfree modelling of skeletal muscles, Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 4(2): 73–85, 2016, doi: 10.1080/21681163.2015.1049712.
18. T. Belytschko, L. Gu, Y. Lu, Fracture and crack growth by element free Galerkin methods, Modelling and Simulation in Materials Science and Engineering, 2(3A): 519–534, 1994, doi: 10.1088/0965-0393/2/3a/007.
19. X. Zhuang, C. Augarde, S. Bordas, Accurate fracture modelling using meshless methods, the visibility criterion and level sets: formulation and 2D modelling, International Journal for Numerical Methods in Engineering, 86(3): 249–268, 2011, doi: 10.1002/nme.3063.
20. S.W. Chi, C.-H. Lee, J.-S. Chen, P.-C. Guan, A level set enhanced natural kernel con- tact algorithm for impact and penetration modeling, International Journal for Numerical Methods in Engineering, 102(3–4): 839–866, 2015, doi: 10.1002/nme.4728.
21. J. Chen, S.W. Chi, C.H. Lee, S.P. Lin, C. Marodon, M.J. Roth, T.R. Slawson, A Multiscale Meshfree Approach for Modeling Fragment Penetration into Ultra High-Strength Concrete, California University, Los Angeles Department of Civil and Enviromental Engineering, 2011.
22. P.W. Randles, L.D. Libersky, Smoothed particle hydrodynamics: some recent improvements and applications, Computer Methods in Applied Mechanics and Engineering, 139(1–4): 375–408, 1996, doi: 10.1016/S0045-7825(96)01090-0.
23. B. Li, A. Kidane, G. Ravichandran, M. Ortiz, Verification and validation of the optimal transportation meshfree (OTM) simulation of terminal ballistics, International Journal of Impact Engineering, 42: 25–36, 2012, doi: 10.1016/j.ijimpeng.2011.11.003.
24. J.-S. Chen, C.-T. Wu, T. Belytschko, Regularization of material instabilities by mesh- free approximations with intrinsic length scales, International Journal for Numerical Methods in Engineering, 47(7): 1303–1322, 2000, doi: 10.1002/(SICI)1097-0207(20000310)47:7<1303::AID-NME826>3.0.CO;2-5.
25. J.-S. Chen, X. Zhang, T. Belytschko, An implicit gradient model by a reproducing kernel strain regularization in strain localization problems, Computer Methods in Applied Mechanics and Engineering, 193(27–29): 2827–2844, 2004, doi: 10.1016/j.cma.2003.12.057.
26. J. Chen, W. Hu, M.A. Puso, Y. Wu, X. Zhang, Strain smoothing for stabilization and regularization of Galerkin meshfree methods, [in:] M. Griebel, M.A. Schweitzer [Eds], Meshfree Methods for Partial Differential Equations III, Vol. 57, pp. 57–75, Springer, Berlin, Heidelberg, 2007.
27. T. Rabczuk, E. Samaniego, Discontinuous modelling of shear bands using adaptive mesh- free methods, Computer Methods in Applied Mechanics and Engineering, 197(6–8): 641–658, 2008, doi: 10.1016/j.cma.2007.08.027.
28. J.-S. Chen, D. Wang, A constrained reproducing kernel particle formulation for shear deformable shell in Cartesian coordinates, International Journal for Numerical Methods in Engineering, 68(2): 151–172, 2006, doi: 10.1002/nme.1701.
29. D. Wang, H. Peng, A Hermite reproducing kernel Galerkin meshfree approach for buckling analysis of thin plates, Computational Mechanics, 51(6): 1013–1029, 2013, doi: 10.1007/ s00466-012-0784-9.
30. G.R. Liu, X. L. Chen, A mesh-free method for static and free vibration analyses of thin plates of complicated shape, Journal of Sound and Vibration, 241(5): 839–855, 2001, doi: 10.1006/jsvi.2000.3330.
31. P. Krysl, T. Belytschko, Analysis of thin plates by the element-free Galerkin method, Computational Mechanics, 17(1): 26–35, 1995, doi: 10.1007/BF00356476.
32. P. Krysl, T. Belytschko, Analysis of thin shells by the element-free Galerkin method, International Journal of Solids and Structures, 33(20–22): 3057–3080, 1996, doi: 10.1016/0020- 7683(95)00265-0.
33. P.S. Jensen, Finite difference techniques for variable grids, Computers & Structures, 2(1–2): 7–29, 1972, doi: 10.1016/0045-7949(72)90020-X.
34. T. Liszka, J. Orkisz, The finite difference method at arbitrary irregular grids and its application in applied mechanics, Computers & Structures, 11(1–2): 83–95, 1980, doi: 10.1016/0045-7949(80)90149-2.
35. L. Gavete, M.L. Gavete, J.J. Benito, Improvements of generalized finite difference method and comparison with other meshless method, Applied Mathematical Modelling, 27(10): 831–847, 2003, doi: 10.1016/S0307-904X(03)00091-X.
36. T. Liszka, An interpolation method for an irregular net of nodes, International Journal for Numerical Methods in Engineering, 20(9): 1599–1612, 1984, doi: 10.1002/nme.1620200905.
37. N. Perrone, R. Kao, A general finite difference method for arbitrary meshes, Computers & Structures, 5(1): 45–57, 1975, doi: 10.1016/0045-7949(75)90018-8.
38. R.A. Gingold, J.J. Monaghan, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Monthly Notices of the Royal Astronomical Society, 181(3): 375–389, 1977, doi: 10.1093/mnras/181.3.375.
39. W.-K. Liu, S. Jun, Y.F. Zhang, Reproducing kernel particle methods, International Journal for Numerical Methods in Fluids, 20(8–9): 1081–1106, 1995, doi: 10.1002/fld.165 0200824.
40. E.J. Kansa, Multiquadrics – A scattered data approximation scheme with applications to computational fluid-dynamics – I surface approximations and partial derivative estimates, Computers & Mathematics with Applications, 19(8–9): 127–145, 1990, doi: 10.1016/0898- 1221(90)90270-T.
41. E.J. Kansa, Multiquadrics – A scattered data approximation scheme with applications to computational fluid-dynamics – II solutions to parabolic, hyperbolic and elliptic partial differential equations, Computers & Mathematics with Applications, 19(8–9): 147–161, 1990, doi: 10.1016/0898-1221(90)90271-K.
42. S.A. Silling, M. Epton, O. Weckner, J. Xu, E. Askari, Peridynamic states and constitutive modeling, Journal of Elasticity, 88(2): 151–184, 2007, doi: 10.1007/s10659-007-9125-1.
43. J.-S. Chen, S. Yoon, C.-T. Wu, Non-linear version of stabilized conforming nodal integration for Galerkin meshfree methods, International Journal for Numerical Methods in Engineering, 53(12): 2587–2615, 2002, doi: 10.1002/nme.338.
44. J.-S. Chen, M. Hillman, M. Rüter, An arbitrary order variationally consistent integration for Galerkin meshfree methods, International Journal for Numerical Methods in Engineering, 95(5): 387–418, 2013, doi: 10.1002/nme.4512.
45. M. Hillman, J.-S. Chen, Nodally integrated implicit gradient reproducing kernel particle method for convection dominated problems, Computer Methods in Applied Mechanics and Engineering, 299: 381–400, 2016, doi: 10.1016/j.cma.2015.11.004.
46. J.-S. Chen, H.-P. Wang, New boundary condition treatments in meshfree computation of contact problems, Computer Methods in Applied Mechanics and Engineering, 187(3-4): 441–468, 2000, doi: 10.1016/S0045-7825(00)80004-3.
47. J. Nitsche, Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind [in German], [in:] Abhandlungen aus dem mathematischen Seminar der Universität Hamburg, 36: 9–15, Springer, 1971, doi: 10.1007/BF02995904.
48. T. Belytschko, Y. Krongauz, D. Organ, M. Fleming, P. Krysl, Meshless methods: an overview and recent developments, Computer Methods in Applied Mechanics and Engineering, 139(1–4): 3–47, 1996, doi: 10.1016/S0045-7825(96)01078-X.
49. S. Li, W.K. Liu, Meshfree and particle methods and their applications, Applied Mechanics Review, 55(1): 1–34, 2002, doi: 10.1115/1.1431547.
50. V.P. Nguyen, T. Rabczuk, S. Bordas, M. Duflot, Meshless methods: a review and computer implementation aspects, Mathematics and Computers in Simulation, 79(3): 763–813, 2008, doi: 10.1016/j.matcom.2008.01.003.
51. T. Belytschko, Y. Krongauz, J. Dolbow, C. Gerlach, On the completeness of meshfree particle methods, International Journal for Numerical Methods in Engineering, 43(5): 785– 819, 1998, doi: 10.1002/(SICI)1097-0207(19981115)43:5<785::AID-NME420>3.0.CO;2-9.
52. N.M. Modak, J.M. Merigó, R. Weber, F. Manzor, J. de Dios Ortúzar, Fifty years of Transportation Research journals: A bibliometric overview, Transportation Research Part A: Policy and Practice, 120: 188–223, 2019, doi: 10.1016/j.tra.2018.11.015.
53. S. Das, A. Dutta, M.A. Brewer, Case study of trend mining in Transportation Research Record articles, Transportation Research Record, 2674(10): 1–14, 2020, doi: 10.1177/ 0361198120936254.
54. A. Torayev, P.C.M.M. Magusin, C.P. Grey, C. Merlet, A.A. Franco, Text mining assisted review of the literature on Li-O2 batteries, Journal of Physics: Materials, 2(4): 044004, 2019, doi: 10.1088/2515-7639/ab3611.
55. Y. Kajikawa, J. Yoshikawa, Y. Takeda, K. Matsushima, Tracking emerging technologies in energy research: Toward a roadmap for sustainable energy, Technological Forecasting and Social Change, 75(6): 771–782, 2008, doi: 10.1016/j.techfore.2007.05.005.
56. F.R. Dayeen, A.S. Sharma, S. Derrible, A text mining analysis of the climate change literature in industrial ecology, Journal of Industrial Ecology, 24(2): 276–284, 2020, doi: 10.1111/jiec.12998.
57. A. Korhonen, D.Ó. Séaghdha, I. Silins, L. Sun, J. Högberg, U. Stenius, Text mining for literature review and knowledge discovery in cancer risk assessment and research, PloS one, 7(4): p. e33427, 2012, doi: 10.1371/journal.pone.0033427.
58. V. Renganathan, Text mining in biomedical domain with emphasis on document clustering, Healthcare Informatics Research, 23(3): 141–146, 2017, doi: 10.4258/hir.2017. 23.3.141.
59. J.J. Monaghan, Smoothed particle hydrodynamics, Reports on Progress in Physics, 68(8): 1703–1759, 2005, doi: 10.1088/0034-4885/68/8/r01.
60. E. Loper, S. Bird, NLTK: the natural language toolkit, arXiv preprint cs/0205028 [cs.CL], 2002.
61. M. Bastian, S. Heymann, M. Jacomy, Gephi: an open source software for exploring and manipulating networks, [in:] Proceedings of the International AAAI Conference on Web and Social Media, 8: 361–362, 2009.
62. R. Alghamdi, K. Alfalqi, A survey of topic modeling in text mining, International Journal on Advanced Computer Science Applications, 6(1): 147–153, 2015.
63. D.M. Blei, A.Y. Ng, M.I. Jordan, Latent Dirichlet allocation, Journal of Machine Learning Research, 3(Jan): 993–1022, 2003.
64. M.J. Cobo, A.G. López-Herrera, E. Herrera-Viedma, F. Herrera, An approach for detecting, quantifying, and visualizing the evolution of a research field: A practical application to the fuzzy sets theory field, Journal of Informetrics, 5(1): 146–166, 2011, doi: 10.1016/j.joi.2010.10.002.
65. J. Fern, A. Rohe, K. Soga, E. Alonso, The Material Point Method for Geotechnical Engineering: A Practical Guide, CRC Press, Boca Raton, 2019.
66. A. de Vaucorbeil, V.P. Nguyen, S. Sinaie, J.Y. Wu, Material point method after 25 years: Theory, implementation and applications, [in:] S.P.A. Bordas, D.S. Balint [Eds], Advances in Applied Mechanics, Vol. 53, p. 185–398, 2020, doi: 10.1016/bs.aams.2019.11.001.
67. H.Y. Hu, J.S. Chen, W. Hu, Weighted radial basis collocation method for boundary value problems, International Journal for Numerical Methods in Engineering, 69(13): 2736–2757, 2007, doi: 10.1002/nme.1877.
68. J.G. Wang, G.R. Liu, A point interpolation meshless method based on radial basis functions, International Journal for Numerical Methods in Engineering, 54(11): 1623–1648, 2002, doi: 10.1002/nme.489.
69. G.R. Liu, G.Y. Zhang, Y.T. Gu, Y.Y. Wang, A meshfree radial point interpolation method (RPIM) for three-dimensional solids, Computational Mechanics, 36(6): 421–430, 2005, doi: 10.1007/s00466-005-0657-6.
70. M. Liu, G.R. Liu, K.Y. Lam, Z. Zong, Smoothed particle hydrodynamics for numerical simulation of underwater explosion, Computational Mechanics, 30(2): 106–118, 2003, doi: 10.1007/s00466-002-0371-6.