Quality of Elements

COMSOL Multiphysics includes several different mesh quality measures. The absolute value of the mesh element quality is always between 0 and 1, where 0.0 represents a degenerated element and 1.0 represents the best possible element. A negative value means a contradiction to the COMSOL Multiphysics numbering convention for mesh element vertices (see Mesh Element Numbering Conventions), and the element is then referred to as an inverted element. The following mesh quality measures are available:

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The skewness (skewness), which is based on the mesh elements’ equiangular skew.

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The maximum angle (maxangle), which is based on the largest angle in the element. If no angle is larger than the largest angle of the corresponding optimal element, the quality is one; otherwise, the measure shows how much larger the angle is. This quality measure is insensitive to element anisotropy.

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The volume versus circumradius (volcircum), which is the default quality measure, is based on the ratios of the inscribed and circumscribed circles’ or spheres’ radii for the simplex corresponding to each corner of the element. If the simplex cannot be clearly determined (an apex of the pyramid, for example), the corresponding corner is excluded from the consideration.

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The volume versus length (vollength), which is based on a quotient of element edge lengths and element volume. This quality measure is primarily sensitive to anisotropy.

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The condition number (condition), which 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.

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The growth rate (growth), which is based on the mesh elements’ local (anisotropic) growth rate.

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The curved skewness (curvedskewness), which is defined as the elementwise product of skewness and reldetjacmin, which is a measure of the deformation when generating the higher-order element.

There is also a custom quality measure (custom), which is based on a user-defined expression for the mesh element quality.

To retrieve the minimal quality, use

double model.component(<ctag>).mesh(<tag>).stat().getMinQuality(type);

double model.component(<ctag>).mesh(<tag>).stat().getMinQuality();

To retrieve the mean quality, use

double model.component(<ctag>).mesh(<tag>).stat().getMeanQuality(type);

double model.component(<ctag>).mesh(<tag>).stat().getMeanQuality();

To calculate a distribution of qualities, use the getQualityDistr method.

int[] model.component(<ctag>).mesh(<tag>).stat().getQualityDistr(type, <size>);

int[] model.component(<ctag>).mesh(<tag>).stat().getQualityDistr(<size>);

The size parameter is a positive integer determining how detailed the distribution is and equals the size of the output array. The distribution can by used to plot a histogram of the element quality. For example, if size equals 10, the first entry in the returned array is the number of elements with quality less than 0.1, and the last entry is the number of elements with quality better than 0.9.

The following methods are available directly on the sequence and provide mesh quality statistics, using the volume versus circumradius quality measure, for the entire geometry: