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
ÿxed 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 ÿxed, moving and multiple ÿxed 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
ÿxed, moving and multiple ÿxed kernel approaches are identical to the ÿxed, moving and multiple
ÿxed least squares approaches. A ÿnite cloud method, which combines collocation with a ÿxed 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; ÿxed kernel technique; reproducing kernel; point collocation; ÿnite
cloud method
1. INTRODUCTION

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

Collections: Engineering; Materials Science