%AVERAGE_MP%

average of a functional based on all non-irreducible monitor points with respect to given material flags

Average of a given functional $ f$ (ExpressionOfIntegrand) with respect to the set $ MP$ of all non-irreducible points (see MONITORPOINTS_CREATION) with given material flags:

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

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

MONITORPOINTS_CREATION($MaterialTag$) = ( %MONITORPOINTS_CREATION_AtBoundary%, CreationFunctional ) ... INTEGRATION($IntInd$) = ( %AVERAGE_MP%, ExpressionOfIntegrand, $MaterialTag$ )

Note: Integration with respect to irreducible monitor points have to be defined by INTEGRATION statements for the point cloud!