cashocs.geometry.quality.SkewnessCalculator

class cashocs.geometry.quality.SkewnessCalculator

Bases: MeshQualityCalculator

Implements the skewness quality measure.

Methods Summary

compute(mesh)

Computes the skewness of the mesh.

Methods Documentation

compute(mesh: fenics.Mesh) → ndarray

Computes the skewness of the mesh.

This measure the relative distance of a triangle’s angles or a tetrahedron’s dihedral angles to the corresponding optimal angle. The optimal angle is defined as the angle an equilateral, and thus equiangular, element has. The skewness lies in \([0,1]\), where 1 corresponds to the case of an optimal (equilateral) element, and 0 corresponds to a degenerate element. The skewness corresponding to some (dihedral) angle \(\alpha\) is defined as

\[1 - \max \left( \frac{\alpha - \alpha^*}{\pi - \alpha*} , \ \frac{\alpha^* - \alpha}{\alpha^* - 0} \right),\]

where \(\alpha^*\) is the corresponding angle of the reference element.

Parameters:

mesh (fenics.Mesh) – The mesh whose quality shall be computed.

Returns:

The element wise skewness of the mesh on process 0.

Return type:

ndarray