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Least-squares meshfree collocation method. (English) Zbl 1359.65274

MSC:
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
Software:
Mfree2D
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References:
[1] S. N. Atluri and S. P. Shen , The Meshless Local Petrov-Galerkin (MLPG) Method ( Tech Science Press , Beijing , 2002 ) . · Zbl 1012.65116
[2] S. N. Atluri and T. Zhu, Comput. Mech. 22, 117 (1998). genRefLink(16, ’rf2’, ’10.1007%252Fs004660050346’); genRefLink(128, ’rf2’, ’000075918000001’);
[3] S. Beissel and T. Belytschko, Comput. Methods Appl. Mech. Eng. 139, 49 (1996). genRefLink(16, ’rf3’, ’10.1016%252FS0045-7825%252896%252901079-1’); genRefLink(128, ’rf3’, ’A1996WA55800003’);
[4] T. Belytschko, Comput. Methods Appl. Mech. Eng. 139, 3 (1996). genRefLink(16, ’rf4’, ’10.1016%252FS0045-7825%252896%252901078-X’); genRefLink(128, ’rf4’, ’A1996WA55800002’);
[5] T. Belytschko, Y. Y. Lu and L. Gu, Int. J. Numer. Methods Eng. 37, 229 (1994). genRefLink(16, ’rf5’, ’10.1002%252Fnme.1620370205’); genRefLink(128, ’rf5’, ’A1994MR17400004’);
[6] P. B. Bochev and M. D. Gunzburger , Least-Squares Finite Element Methods ( Springer , New York , 2009 ) . · Zbl 1168.65067
[7] P. Breitkopf, G. Touzot and P. Villon, Comput. Mech. 25, 199 (2000). genRefLink(16, ’rf7’, ’10.1007%252Fs004660050469’); genRefLink(128, ’rf7’, ’000086461200008’);
[8] J. S. Chen, Comput. Methods Appl. Mech. Eng. 139, 195 (1996). genRefLink(16, ’rf8’, ’10.1016%252FS0045-7825%252896%252901083-3’); genRefLink(128, ’rf8’, ’A1996WA55800007’);
[9] J. S Chen, Int. J. Numer. Methods Eng. 50, 435 (2001). genRefLink(16, ’rf9’, ’10.1002%252F1097-0207%252820010120%252950%253A2%253C435%253A%253AAID-NME32%253E3.0.CO%253B2-A’); genRefLink(128, ’rf9’, ’000166388600009’);
[10] C. A. Duarte and J. T. Oden, Comput. Methods Appl. Mech. Eng. 139, 237 (1996). genRefLink(16, ’rf10’, ’10.1016%252FS0045-7825%252896%252901085-7’); genRefLink(128, ’rf10’, ’A1996WA55800009’);
[11] F. Gother and W. K. Liu, Comput. Methods Appl. Mech. Eng. 163, 205 (1998). genRefLink(128, ’rf11’, ’000076740200014’);
[12] S. Hao, H. S. Park and W. K. Liu, Int. J. Numer. Methods Eng. 53, 1937 (2002). genRefLink(16, ’rf12’, ’10.1002%252Fnme.368’); genRefLink(128, ’rf12’, ’000174049900008’);
[13] Jiang and Bo-nan , The Least-Squares Finite Element Method. Theory and Applications in Computational Fluid Dynamics and Electromagnetics ( Springer , Heidelberg , 1998 ) . · Zbl 0904.76003
[14] B. N. Jiang and J. Wu, Int. J. Numer. methods Eng. 53, 603 (2009). genRefLink(128, ’rf14’, ’000173130000006’);
[15] Y. Krongauz and T. Belytschko, Comput. Methods Appl. Mech. Eng. 131, 133 (1996). genRefLink(16, ’rf15’, ’10.1016%252F0045-7825%252895%252900954-X’); genRefLink(128, ’rf15’, ’A1996UR44100006’);
[16] K. C. Kwon, Comput. Mech. 30, 196 (2003). genRefLink(16, ’rf16’, ’10.1007%252Fs00466-002-0379-y’); genRefLink(128, ’rf16’, ’000181561900003’);
[17] Kunle, M. [2001] Entwicklung und Untersuchung von Moving Least Square Verfahren zur Numerischen Simulation Hydrodynamischer Gleichungen, Dissertation, Fakultat fur Physik, Eberhard-Karls-Universitat zu Tubingen .
[18] P. Lancaster and K. Salkauskas, Math. Comput. 37, 141 (1981). genRefLink(16, ’rf18’, ’10.1090%252FS0025-5718-1981-0616367-1’); genRefLink(128, ’rf18’, ’A1981MB34000012’);
[19] Li, S. F. and Liu, W. K. [2002] ”Meshfree particle methods and their applications,” Appl. Mech. Rev. 55, 1-34. ”Particle methods and their applications,” Appl. Mech. Rev. 55, 1-34 .
[20] S. F. Li and W. K. Liu , Meshfree Particle Methods ( Springer , Berlin , 2004 ) . · Zbl 1073.65002
[21] T. J. Liszka, C. A. M. Duarte and W. W. Tworzydlo, Comput. Methods Appl. Mech. Eng. 139, 263 (1996). genRefLink(16, ’rf21’, ’10.1016%252FS0045-7825%252896%252901086-9’); genRefLink(128, ’rf21’, ’A1996WA55800010’);
[22] T. J. Liszka and J. Orkisz, Comput. Struct. 11, 83 (1980). genRefLink(16, ’rf22’, ’10.1016%252F0045-7949%252880%252990149-2’); genRefLink(128, ’rf22’, ’A1980JP72900009’);
[23] W. K. Liu, S. Jun and Y. F. Zhang, Int. J. Numer. Methods Fluid. 20, 1081 (1995). genRefLink(16, ’rf23’, ’10.1002%252Ffld.1650200824’); genRefLink(128, ’rf23’, ’A1995QX11300024’);
[24] G. R. Liu and Y. T. Gu, Int. J. Numer. Methods Eng. 50, 937 (2001). genRefLink(16, ’rf24’, ’10.1002%252F1097-0207%252820010210%252950%253A4%253C937%253A%253AAID-NME62%253E3.0.CO%253B2-X’); genRefLink(128, ’rf24’, ’000166732600010’);
[25] G. R. Liu , Mesh Free Methods: Moving Beyond the Finite Element Method , 2nd edn. ( CRC Press , 2009 ) . genRefLink(16, ’rf25’, ’10.1201%252F9781420082104’);
[26] G. R. Liu and Y. T. Gu , An Introduction of Meshfree Methods and Their Programming ( Springer , Dordrecht , 2005 ) .
[27] W. K. Liu, R. A. Uras and Y. Chen, J. Appl. Mech. 64, 861 (1997). genRefLink(16, ’rf27’, ’10.1115%252F1.2788993’); genRefLink(128, ’rf27’, ’000071478100018’);
[28] Y. Y. Lu , T. Belytschko and M. Tabbara , Comput. Methods Appl. Mech. Eng. 126 , 131 . genRefLink(16, ’rf28’, ’10.1016%252F0045-7825%252895%252900804-A’); genRefLink(128, ’rf28’, ’A1995TG12500007’);
[29] L. B. Lucy, Astronaut. J. 8, 1013 (1977).
[30] H. MacMillan, M. D. Gunzburger and J. Burkardt, Numer. Math. Theor. Methods Appl. 1, 29 (2008). genRefLink(128, ’rf30’, ’A1948YA26300003’);
[31] J. M. Melenk and I. Babuška, Comput. Methods Appl. Mech. Eng. 139, 289 (1997). genRefLink(16, ’rf31’, ’10.1016%252FS0045-7825%252896%252901087-0’); genRefLink(128, ’rf31’, ’A1996WA55800011’);
[32] Y. X. Mukherjee and S. Mukherjee, Comput. Mech. 19, 264 (1997). genRefLink(16, ’rf32’, ’10.1007%252Fs004660050175’); genRefLink(128, ’rf32’, ’A1997WU69300002’);
[33] T. Nagashima, Int. J. Numer. Methods Eng. 39, 341 (1999).
[34] B. Nayroles, G. Touzot and P. Villon, Comput. Mech. 10, 307 (1992). genRefLink(16, ’rf34’, ’10.1007%252FBF00364252’);
[35] H. Netuzhylov and A. Zilian, Int. J. Numer. Methods Eng. 80, 355 (2009). genRefLink(16, ’rf35’, ’10.1002%252Fnme.2638’); genRefLink(128, ’rf35’, ’000270931400005’);
[36] E. Onate, O. C. Zienkiewicz and R. L. Taylor, Int. J. Numer. Methods Eng. 39, 3839 (1996). genRefLink(16, ’rf36’, ’10.1002%252F%2528SICI%25291097-0207%252819961130%252939%253A22%253C3839%253A%253AAID-NME27%253E3.0.CO%253B2-R’); genRefLink(128, ’rf36’, ’A1996VR51500005’);
[37] S. H Park, K. C. Kwon and S. K. Youn, Int. J. Numer. Methods Eng. 56, 1374 (2003).
[38] S. H. Park, K. C. Kwon and S. K. Youn, Int. J. Numer. Methods Eng. 58, 1213 (2003). genRefLink(16, ’rf38’, ’10.1002%252Fnme.817’); genRefLink(128, ’rf38’, ’000185985700005’);
[39] S. H. Park and S. K. Youn, Int. J. Numer. Methods Eng. 52, 997 (2001). genRefLink(16, ’rf39’, ’10.1002%252Fnme.248’); genRefLink(128, ’rf39’, ’000171912600006’);
[40] G. Yagawa and T. Yamada, Comput. Mech. 8, 383 (1996).
[41] G. Yagawa, Int. J. Numer. Methods Eng. 60, 69 (2004). genRefLink(16, ’rf41’, ’10.1002%252Fnme.955’); genRefLink(128, ’rf41’, ’000221236300006’);
[42] Q. X. Yang , Elementfree Methods in Engineering Electromagnetics ( Science , Beijing, China , 2008 ) .
[43] X. Zhang and Y. Liu , Meshless Methods ( Tsinghua University Press , Beijing , 2004 ) .
[44] X. Zhang, Int. J. Numer. Methods Eng. 51, 1089 (2001). genRefLink(16, ’rf44’, ’10.1002%252Fnme.200’); genRefLink(128, ’rf44’, ’000169862000005’);
[45] X. K. Zhang, K. C. Kwon and S. K. Youn, Comput. Phys. 206, 182 (2005). genRefLink(16, ’rf45’, ’10.1016%252Fj.jcp.2004.11.033’);
[46] T. Zhu and S. N. Atluri, Comput. Mech. 21, 211 (1998). genRefLink(16, ’rf46’, ’10.1007%252Fs004660050296’); genRefLink(128, ’rf46’, ’000073614200002’);
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