Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Least-Squares Meshfree Method and Integration Error

최소 제곱 무요소법과 적분 오차

  • Published : 2001.10.01
Download PDF
⟨ Previous Next ⟩

Abstract

Least-squares meshfree method is presented. Conventional meshfree methods based on the Galerkin formulation suffer from inaccurate numerical integration. Least-squares formulation exhibits rather different integration-related characteristics. It is demonstrated through numerical examples that least-squares formulation is much more robust to integration errors than the Galerkin's. Therefore efficient meshfree methods can be devised by combining very simple integration algorithms and least-squares formulation.

Keywords

References

  1. Belytschko, T., Lu, Y.Y. and Gu, L., 1994, 'Element-Free Galerkin Methods,' Int. J. Numer. Meth. Engng., Vol. 37, pp. 229-256 https://doi.org/10.1002/nme.1620370205
  2. Liu, W.K., Jun, S. and Zhang, Y.F., 1995, 'Reproducing Kernel Particle Methods,' Int. J. Numer. Meth. Fluids, Vol. 20, pp. 1081-1106 https://doi.org/10.1002/fld.1650200824
  3. Duarte, C.A. and Oden, J.T., 1995, 'Hp Clouds - A Meshless Method to Solve Boundary-Value Problems,' Technical Report 95-05, TICAM, University of Texas at Austin
  4. Lancaster, P. and Salkauskas, K., 1981, 'Surfaces Generated by Moving Least-Squares Methods,' Mathematics of Computation, Vol. 37, pp. 141-158 https://doi.org/10.2307/2007507
  5. Dolbow, J. and Belytschko, T., 1999, 'Numerical Integration of the Galerkin Weak Form in Meshfree Methods,' Computational Mechanics, Vol. 23 pp. 219-230 https://doi.org/10.1007/s004660050403
  6. Beissel, S. and Belytschko, T., 1996, 'Nodal Integration of the Element-Free Gralerkin Method,' Comput. Methods Appl. Mech. Engrg., Vol. 139, pp. 49-74 https://doi.org/10.1016/S0045-7825(96)01079-1
  7. Atluri, S.N. and Zhu, T., 1998, 'A New Meshless Local Petrov-Galerkin (MLPG) Approach in Computational Mechanics,' Computational Mechanics, Vol. 22, pp. 117-127 https://doi.org/10.1007/s004660050346
  8. Onate, E., Zienkiewicz, O.C. and Taylor, R.L., 1996, 'A Finite Point Method in Computational Mechanics. Applications to Convective Transport and Fluid Flow,' Int. J. Numer. Meth. Engng., Vol. 39, pp. 3839-3866 https://doi.org/10.1002/(SICI)1097-0207(19961130)39:22<3839::AID-NME27>3.0.CO;2-R
  9. Breitkopf, P., Touzot, G. and Villon, P., 2000, 'Double Grid Diffuse Collocation Method,' Computational Mechanics, Vol. 25, pp. 199-206 https://doi.org/10.1007/s004660050469
  10. Jiang, B.N., 1998, 'The Least-Squares Finite Element Method - Theory and Applications in Computational Fluid Dynamics and Electromagnetics, Berlin, Spring-Verlag
  11. 박상훈, 2001, '최소 제곱 무요소법의 오차추정 및 적응적 기법에 관한 연구,' 한국과학기술원 박사학위논문