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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng. 2000; 47:1083}1121
 

Summary: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Int. J. Numer. Meth. Engng. 2000; 47:1083}1121
A point collocation method based on reproducing
kernel approximations
N. R. Aluru*
Beckman Institute and Department of General Engineering, ;niversity of Illinois at ;rbana-Champaign,
;rbana, Ił 61801, ;.S.A.
SUMMARY
A reproducing kernel particle method with built-in multiresolution features in a very attractive meshfree
method for numerical solution of partial di!erential equations. The design and implementation of a
Galerkin-based reproducing kernel particle method, however, faces several challenges such as the issue of
nodal volumes and accurate and e$cient implementation of boundary conditions. In this paper we present
a point collocation method based on reproducing kernel approximations. We show that, in a point
collocation approach, the assignment of nodal volumes and implementation of boundary conditions are not
critical issues and points can be sprinkled randomly making the point collocation method a true meshless
approach. The point collocation method based on reproducing kernel approximations, however, requires
the calculation of higher-order derivatives that would typically not be required in a Galerkin method,
A correction function and reproducing conditions that enable consistency of the point collocation
method are derived. The point collocation method is shown to be accurate for several one and
two-dimensional problems and the convergence rate of the point collocation method is addressed.

  

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

 

Collections: Engineering; Materials Science