7.2.0.1 Definition:

We define an index allowing to quickly judge if the mesh is in agreement with the metric field. Let us note $l_i$ the length of the edge $e_i$ in the metric. The efficiency index of a mesh is defined as the exponentiel of the mean between the difference with $1$ of all the lengths $l_i$ normalized by the number of mesh edges. Let us call $\tau$ this index:

$$\tau = \exp\left(\frac{1}{ne} \displaystyle{\sum_{i=1}^{ne} e_i}\right)$$

with $e_i = l_i -1$ si $l_i<1$ and $e_i = \displaystyle \frac{1}{l_i} -1$ if $l_i>1$ and $ne$ the number of mesh edges.