quadmeshquality.f

Recall that the smoothed position of a vertex node is only accepted if the quality of its ball did not get worse. In analogy, the smoothed position of a mnidnode will only be accepted if the quality of its shell does not get worse. For the quality measure of a quadratic element the largest difference of the Jacobian determinant at the integration points will be taken as measure. Recall that the 10-node tetrahedral element has 4 integration points. The quality of quadratic element $i$ is now defined as:

$$Q_i^*=\left ( \frac{J_{\text{max}}-J_{\text{min}}}{J_{\text{max}}... ...\text{min}}) \frac{<-J_{\text{min}}>}{\left \vert J_{\text{min}} \right \vert},$$ (718)

where $<x>=x$ if $x>0$ and $<x>=0$ if $x \le 0$. The second term in the above equation takes precedence as soon as any Jacobian determinant in the element is negative.