Biomedical Engineering Reference
In-Depth Information
Fig. 4.8
2D weight functions first order partial derivatives. W3 cubic spline. W4 quartic spline
It is possible to construct a weight function with any desire order of continuity.
A detailed description on efficient methodologies to construct weight functions can
be found in the literature [
5
,
17
].
4.3.3 MLS Shape Function Properties
4.3.3.1 Consistency
The shape function ability to reproduce the complete order of an unknown poly-
nomial function is defined as consistency. The consistency of the MLS approxi-
mation depends on the complete order of the polynomial basis used in the
Eq. (
4.6
), therefore a shape function possess C
m
consistency when the used
polynomial basis possess m monomials [
18
]. The MLS shape function consistency
can be easily demonstrated [
5
,
18
]. Consider a field defined by the following
complete polynomial function,
