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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2001; 50:23732410
 

Summary: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Int. J. Numer. Meth. Engng 2001; 50:2373­2410
Finite cloud method: a true meshless technique based on a
˙xed reproducing kernel approximation
N. R. Aluru
and Gang Li
Beckman Institute and Department of General Engineering; University of Illinois at Urbana-Champaign;
Urbana; IL 61801; U.S.A.
SUMMARY
We introduce ˙xed, moving and multiple ˙xed kernel techniques for the construction of interpolation
functions over a scattered set of points. We show that for a particular choice of nodal volumes, the
˙xed, moving and multiple ˙xed kernel approaches are identical to the ˙xed, moving and multiple
˙xed least squares approaches. A ˙nite cloud method, which combines collocation with a ˙xed kernel
technique for the construction of interpolation functions, is presented as a true meshless technique for
the numerical solution of partial di erential equations. Numerical results are presented for several one-
and two-dimensional problems, including examples from elasticity, heat conduction, thermoelasticity,
Stokes ow and piezoelectricity. Copyright ? 2001 John Wiley & Sons, Ltd.
KEY WORDS: meshless method; ˙xed kernel technique; reproducing kernel; point collocation; ˙nite
cloud method
1. INTRODUCTION

  

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

 

Collections: Engineering; Materials Science