Summary: A boundary cloud method with a cloud-by-cloud polynomial basis
, N.R. Alurub,*
Department of Mechanical and Industrial Engineering, Beckman Institute for Advanced Science and Technology,
University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Department of General Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign,
Urbana, IL 61801, USA
Received 18 April 2002; revised 6 September 2002; accepted 18 September 2002
We have recently presented a boundary cloud method (BCM) [Comput. Meth. Appl. Mech. Engng 191 (2002) 2337], which combines
boundary integral formulations with scattered point interpolation techniques. A generalized least-squares approach, which requires
information about the outward normal to the boundary, is employed to construct interpolation functions. Since an outward normal is not well
defined for geometries with corners for 2D problems (or for corners and edges for 3D problems), points could not be placed at corners when
discretizing the surface of the object. In this paper, we introduce a new implementation of the BCM, which uses a varying base interpolating
polynomial to construct interpolation functions. The key idea is to define an appropriate polynomial basis which ensures linear completeness.
The polynomial basis can change from cloud to cloud depending on the definition of the cloud at each point. The new implementation can
handle points at corners and is much simpler and at least an order of magnitude faster compared to our original implementation. The original
implementation can be more accurate and can give higher order convergence rates, but is limited because it cannot handle points at corners.