A singularity-avoiding moving least squares scheme for two-dimensional unstructured meshes
Samuel KM Chenoweth, Julio Soria, Andrew Ooi
JOURNAL OF COMPUTATIONAL PHYSICS | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2009
Moving least squares interpolation schemes are in widespread use as a tool for numerical analysis on scattered data. In particular, they are often employed when solving partial differential equations on unstructured meshes, which are typically needed when the geometry defining the domain is complex. It is known that such schemes can be singular if the data points in the stencil happen to be in certain special geometric arrangements, however little research has specifically addressed this issue. In this paper, a moving least squares scheme is presented which is an appropriate tool for use when solving partial differential equations in two dimensions, and the precise conditions under which sin..View full abstract
Awarded by Australian Research Council
The authors would like to acknowledge the support of the Australian Research Council for this research through Grant DP0556098.