PL EN


Preferences help
enabled [disable] Abstract
Number of results
2015 | 128 | 1A | A-50-A-55
Article title

Galerkin Versions of Nonsingular Trefftz Method Derived from Variational Formulations for 2D Laplace Problem

Content
Title variants
Languages of publication
EN
Abstracts
EN
In the paper, application of the Trefftz complete functions and Kupradze functions in two variational formulations is compared. They are applied in the original formulation and in the inverse one to the solution of boundary value problems of two-dimensional Laplace's equation. In these formulations, both solution and weighting functions are assumed to be of the same type, either the Trefftz function or the Kupradze function. Thus Galerkin versions of the methods are considered. All methods lead to the BEM and they are nonsingular. The relationship between the groups of methods of the original and inverse formulations is noticed. Numerical experiments are conducted for the Motz's problem. The accuracy and simplicity of the methods are discussed. All methods give comparable results. Since they are nonsingular, they may be successfully applied to solving boundary problems.
Keywords
EN
Contributors
author
  • Laboratory of Acoustics, The Faculty of Electrical and Computer Engineering, Rzeszow University of Technology, Powstańców Warszawy 12, 35-959 Rzeszow, Poland
  • Department of Computer Engineering in Management, The Faculty of Management, Rzeszow University of Technology, Powstańców Warszawy 12, 35-959 Rzeszow, Poland
References
  • [1] E. Trefftz, Proc. 2nd Int. Cong. Appl. Mech., Zurich 1926, p. 131
  • [2] P.K. Banerjee, R. Butterfield, Boundary Element Methods in Engineering Science, McGraw-Hill Book, London 1981, e-book 2007
  • [3] L.C. Wrobel, The Boundary Element Method, Vol. 1, Appliacation in Thermo-Fluids and Acoustics, John Wiley & Sons, Chichester 2002
  • [4] R.D. Ciskowski, C.A. Brebbia, Boundary element methods in acoustics, Computational Mechanics Publications, Southampton 1991
  • [5] I. Herrera, Boundary methods; An algebraic theory, Pitman Publishing, Boston 1984
  • [6] A.P. Zieliński, Adv. Eng. Softw. 24, 147 (1995), doi: 10.1016/0965-9978(95)00066-6
  • [7] I. Herrera, Numer. Meth. Partial Differ. 16, 561 (2000), doi: 10.1002/1098-2426(200011)16:6<561::AID-NUM4>3.0.CO;2-V
  • [8] Z-C. Li, L-J. Young, H-T. Huang, Y-P. Liu, A.H.-D. Cheng, EABE 34, 248 (2010), doi: 10.1016/j.enganabound.2009.10.001
  • [9] A. H-D. Cheng, T-T. Lu, Trefftz and collocation methods, WIT Press, Southampton 2006
  • [10] Zi-Cai Li, T-T. Lu, H-T. Hu, A.H.-D. Cheng, Trefftz and collocation methods, WIT Press, Southampton 2008
  • [11] E. Kita, N. Kamiya, Adv. Eng. Softw. 24, 3 (1995), doi: 10.1016/0965-9978(95)00067-4
  • [12] R. Schaback in Adaptive numerical solution of MFS systems, Eds. C.S. Chen, A. Karegeorghis, Y.S. Smyrlis, Dynamic Publishers, Atlanta 2008, p. 1
  • [13] J.T. Chen, C.S. Wu, Y.T. Lee, K.H. Chen, Comput. Math. Appl. 53, 851 (2007), doi: 10.1016/j.camwa.2005.02.021
  • [14] P. Gamallo, R.J. Astley, Int. J. Numer. Meth. Engng. 71, 406 (2007), doi: 10.1002/nme.1948
  • [15] A. Brański, M. Borkowski, D. Borkowska, EABE 36, 505 (2012), doi: 10.1016/j.enganabound.2011.11.004
  • [16] Kok Hwa Yu, A. Halim Kadarman, H. Djojodihardio, EABE 34, 884 (2010), doi: 10.1016/j.enganabound.2010.05.001
  • [17] R. Henda, Advanced process simulation, Method of Weighted Residuals (lecture), Lund, Sweden 2006 http://staff.chemeng.lth.se/ berntn/cpdc/courses/adprocsimmaterial-filer/lecture_mwr.pdf
  • [18] A. Brański, Numerical methods for solving boundary problems, survey and classification, Publishing House Rzeszow University of Technology, Rzeszow 2013 (in Polish)
  • [19] C.A. Brebbia, J.C.F. Telles, L.C. Wrobel, Boundary Element Techniques, Springer-Verlag, Berlin, New York 1984
  • [20] D.J. Cartwright, Underlying principles of the boundary element method, WIT Press, Southampton 2001
  • [21] Y.K. Cheung, W.G. Jin, O.C. Zienkiewicz, Comm. Appl. Num. Meth. 5, 159 (1989), doi: 10.1002/cnm.1630050304
  • [22] W.G. Jin, Y.K. Cheung, O.C. Zienkiewicz, Int. J. Numer. Meth. Engng 30, 1147 (1990), doi: 10.1002/nme.1620300605
  • [23] Y.K. Cheung, W.G. Jin, O.C. Zienkiewicz, Int. J. Numer. Meth. Engng 32, 63 (1991), doi: 10.1002/nme.1620320105
  • [24] Zi-Cai Li, T-T. Lu, H-T. Huang, A.H.-D. Cheng, Numer. Meth. Part. D. E. 23, 93 (2007), doi: 10.1002/num.20159
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv128n1a09kz
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.