COMSOL 6.2 - Statistics

Use the stat() method on the meshing sequence to determine the number of elements of different types and the quality of elements. For information about number of entities, see Information on the Geometric Model.

The stat() method returns an object with a collection of methods that can be queried for statistical information about the current mesh. There is also a selection,

which is used to select geometric entities for which the statistics is calculated. The default selection is the entire geometry. The methods described below also exist directly on the meshing sequence. These methods always return statistics for the entire geometry.

Statistics can be requested per element type. The type is given as a string, denoted type, and the possible types are listed in the following table.

Table 4-4: Element Types.
String	Element	Element dimension
vtx	Vertex element	0
edg	Edge element	1
tri	Triangular element	2
quad	Quadrilateral element	2
tet	Tetrahedral element	3
pyr	Pyramid element	3
prism	Prism element	3
hex	Hexahedral element	3
all	All elements of maximal dimension in the selection

Table 4-4: Element Types.

Quadrilateral element

All elements of maximal dimension in the selection

The parameter string all gives statistics for all elements with the same dimension as the maximal dimension of the current selection. For example, if the entire geometry is selected in 2D, the parameter all provides combined statistics for triangular and quadrilateral elements.

To specify the mesh quality measure to use, use the setQualityMeasure method. For example,

model.component(<ctag>).mesh(<tag>).stat().setQualityMeasure("maxangle")

To get the current mesh quality measure, use the getQualityMeasure method:

String model.component(<ctag>).mesh(<tag>).stat().getQualityMeasure()

Table 4-5: Mesh Quality Measures.
NAME	Description
skewness	Skewness. This measure is based on a calculation of the mesh elements’ equiangular skew.
maxangle	Maximum angle. This measure is based on the largest angle in the element.
volcircum	Volume versus circumradius. This measure is based on a quotient of the element volume and the radius of the circumscribed sphere (or circle) of the element.
vollength	Volume versus length. This measure is based on a quotient of element edge lengths and element volume.
condition	Condition number. This measure is based on the element dimension divided by the condition number (in the Frobenius norm) of the matrix transforming the element to a reference element.
growth	Neighbor growth rate. This measure is based on a mesh element growth rate calculation.
curvedskewness	Curved skewness. This measure is defined as the elementwise product of skewness and reldetjacmin, which is a measure of the deformation when generating the higher-order element.
custom	A custom mesh quality expression.

Table 4-5: Mesh Quality Measures.

NAME

Description

skewness

Skewness. This measure is based on a calculation of the mesh elements’ equiangular skew.

maxangle

Maximum angle. This measure is based on the largest angle in the element.

volcircum

Volume versus circumradius. This measure is based on a quotient of the element volume and the radius of the circumscribed sphere (or circle) of the element.

vollength

Volume versus length. This measure is based on a quotient of element edge lengths and element volume.

condition

Condition number. This measure is based on the element dimension divided by the condition number (in the Frobenius norm) of the matrix transforming the element to a reference element.

growth

Neighbor growth rate. This measure is based on a mesh element growth rate calculation.

curvedskewness

Curved skewness. This measure is defined as the elementwise product of skewness and reldetjacmin, which is a measure of the deformation when generating the higher-order element.

custom

A custom mesh quality expression.