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New approximations and collocation schemes in the finite cloud method
 

Summary: New approximations and collocation schemes in the
finite cloud method
Xiaozhong Jin a
, Gang Li b
, N.R. Aluru a,*
a
Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Campaign,
Beckman Institute for Advanced Science and Technology, 405 North Mathews Avenue, Urbana, IL 61801, United States
b
Beckman Institute, UIUC, United States
Accepted 8 October 2004
Available online 9 March 2005
Abstract
The finite cloud method (FCM) [Int. J. Numer. Methods in Eng. 50(10) (2001) 2373] is a meshless technique com-
bining a fixed kernel approximation of the unknown function(s) with a point collocation discretization of the governing
PDEs. The meshless approximation and the collocation discretization are the two major steps in FCM. Since the quality
of the numerical solution depends on the quality of the meshless approximation functions or shape functions and the
discretization scheme employed, in this paper, we propose several improvements to the construction of meshless shape
functions and compare several collocation schemes within the framework of the FCM. The improvements to the shape
functions are combined with various collocation schemes to solve several 2-D Poisson and elastostatic examples. The

  

Source: Aluru, Narayana R. - Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign

 

Collections: Engineering; Materials Science