Mesh quality

Menu: Mesh->Mesh quality

This option opens a window that shows information about the quality of the mesh elements.

There are ten criteria used to measure the quality of the elements, or to provide with some measure of the mesh:

• Minimum angle: The quality criterion is the minimum angle in surface elements and the minimum dihedral angle for volume elements. This means that elements with a small angle are considered to be of a worse quality than ones with bigger angles.
• Maximum angle: This gives the maximum angle for every element. Elements with bigger angles are considered worse. Typically, the Minimum angle criterion is good for qualifying triangles and tetrahedra and the Maximum angle criterion is good for quadrilaterals and hexahedra
• Element vol: The quality criterion is the size of elements (distance for lines, area for surfaces and volume for volumes). Elements with small "volume" are considered worse.
• Minimum edge: The quality criterion is the size of the smaller edge of each element. Elements with smaller edges are considered worse.
• Maximum edge: The quality criterion is the size of the largest edge of each element. Elements with bigger edges are considered worse.
• Shape quality: The quality criterion measures the likeness of the element to the reference one (an equilateral triangle in the case of triangles, a regular tetrahedron in the case of tetrahedra, a square in the case of quadrilaterals and a cube in the case of hexahedra). Its value is 1 for a perfect element (the reference one), and it decreases as the element becomes worse. If it reaches a negative figure it means that the element has a negative Jacobian at some point. The mathematical expression of this quality measure for each type of element is as follows.
• • Triangles: The shape quality (q) of triangles is measured as

where Area is the area of the triangle, and l_i (i=1..3) are the lengths of the triangle's edges.

• • Tetrahedra: The shape quality (q) of tetrahedra is measured as

where Volume is the volume of the tetrahedron, and l_i (i=1..6) are the lengths of the tetrahedron's edges.

• • Quadrilaterals: The shape quality (q) of quadrilaterals is measured as the quality of the worst quality node. The quality of a node (q_n) is given by

where l_1 and l_2 are the lengths of concurrent edges of the node, and Area_n is the area of a fictitious parallelogram, made with these two edges.

• • Hexahedra: The shape quality (q) of hexahedra is measured as the quality of the worst quality node. The quality of a node (q_n) is given by

where l_1, l_2, l_3, A_1, A_2, A_3 are the lengths and areas of concurrent edges and faces of the node, and Volume_n is the volume of a fictitious parallelepiped, made with these concurrent faces.

• Minimum Jacobian: The quality criterion is the value of the minimum Jacobian between the Jacobians calculated at each element Gauss point. If there are elements with negative Jacobians, problems may be encoutered in some calculation processes.
• Radius: This option is only available for sphere and circle elements. It represents the radius of the element.
• Space Filling: This option is only available for sphere elements. It tries to represent the void space around each sphere.
• Num neighgours: This option is only available for sphere elements. It represents the number of neighbours each sphere has.

There are two visualization modes:

1. Normal: The graph shows the number of elements that have an angle of a certain size.
2. Accumulated: The graph shows the number of elements which have an angle of a given size or smaller.

In the MeshQuality window, if you double click on a value, the elements below this value are selected in red. These selected elements can be sent to a layer using the Send To Layer button in the Mesh Quality window.

EXAMPLE

In this example we are studying the mesh using the minimum angle criterion. We can see that between 1935 and 2902 elements approximately of our mesh have an angle of less than 43.4 degrees. If we double-click on the graphic, the elements which have an angle smaller than 43.4 degrees will be selected.