%AVERAGE_INT%

average of a functional based on all MESHFREE points with respect to given material flags

Average of a given functional $ f$ (ExpressionOfIntegrand) with respect to the set $ P$ of all MESHFREE points with given material flags:

\begin{align} I_{\text{Avg}} = \frac{1}{\#P} \sum_{i \in P} f_i,\end{align}

where $ \#P$ denotes the number of points in $ P$. Example:

begin_alias{} "Alias1" = " ... MAT$MaterialTag1$ ... " # definition of Alias1 "Alias2" = " ... MAT$MaterialTag2$ ... " # definition of Alias2 end_alias INTEGRATION($IntInd$) = ( %AVERAGE_INT%, ExpressionOfIntegrand, $MaterialTag1$, $MaterialTag2$ )

DROPLETPHASE

For DROPLETPHASE points, the parcel concept is automatically taken into account, so that

\begin{align} I_{\text{Avg}} = \frac{\sum_{i \in P} n_i \cdot f_i}{\sum_{i \in P} n_i}\end{align}

where $ n_i$ corresponds to the multiplicity stored in %ind_mult%.