A new release version of the PrePoMax contains the following FEM features:
- a tool to check the element quality was added: Model → Element → Element Quality
- bug fixes
And the following user features:
- bug fixes
8 Likes
Currently, the element quality tool supports all Gmsh quality metrics. The names of the metrics are the same as in Gmsh. I was unable to find any official explanation of the meanings of the metrics (Element quality metrics (#3055) · Issues · gmsh / gmsh · GitLab) but I would like to add some descriptions to the PrePoMax. If anyone has any experience with the metrics, please help:
minDetJac → minimal Jacobian determinant
maxDetJac → maximal Jacobian determinant
minSJ → minimal scaled Jacobian (?)
minSICN → minimal signed inverted condition number (?)
minSIGE → signed inverted gradient error (?)
gamma → ratio of the inscribed to the circumscribed sphere radius
innerRadius → inner radius (?)
outerRadius → outer radius (?)
minIsotropy → minimum isotropy measure (?)
angleShape → angle shape measure (?)
minEdge → minimum straight edge length (?)
maxEdge → maximum straight edge length (?)
volume → element volume
4 Likes
as i understand basically, Gmsh implementing mesh quality of quadratic element which probably another mesher don’t have. Internally an ideal and references element is predefined for triangular/tetra and quadrilateral/hexa, then actual mesh generated is mapped or compared. Explanation may not simple and it can be complex than linear element as available by another mesher. More details available in documentation from the authors (link) covering Scaled Jacobian (SJ), Inverted of Condition Number (ICN), and Inverted Gradient Error (IGE). Another metrics may be generic, innerRadius and outerRadius is related to inscribed and circumscribe of circle (tria//quad) or sphere(tetra/hexa), minIsotropy is ratio between edge length of neighbor, element, minEdge and maxEdge is length of an edge in element similar to mesh preset. However, i have not known about angleShape it’s usually referring to angle between two adjacent side of element.
many thanks for implementation in PrePoMax, displaying by color spectrum based on each element value can be interesting as available in Gmsh.
3 Likes
I will add color spectrum results in the future. For that, a new visualization style is needed.
2 Likes
brief description is available also from Gmsh webs QA,
- What is the signification of SICN, Gamma and SIGE in Tools->Statistics?They measure the quality of the elements’ shape in a mesh. They are defined for all 2D and 3D element types, except Gamma which is not defined for hexes and pyramids. The ‘S-’ of SICN and SIGE stands for ‘Signed’. Those two measures actually give two information on an element: Their absolute value gives the element’s shape quality while their sign gives the element validity. In other words, negative values of SICN and SIGE indicate tangled elements. The pure quality part of the measures take values between 0 and 1, with 1 corresponding to the best shape.The measures are computed for 3D elements if any, otherwise for 2D elements. Given values are the average, the minimum and the maximum among elements. Graphs plot the number of elements vs. the quality measure.Meaning of the measures:
- ‘(S-)ICN’ stands for (Signed-) Inverse Condition Number. Low-ICN elements influence negatively the condition number of the stiffness matrix which, as a result, can introduce roundoff errors, or significantly reduce the convergence speed of iterative methods.
- ‘(S-)IGE’ stands for (Signed-) Inverse Gradient Error. Low-IGE elements influence negatively the error on the gradient of the FE solution. For hexahedra, the measure is the well-known “scaled Jacobian” as defined in the hexahedral community.
- For triangles and tetrahedra, ‘Gamma’ is equal to the ratio “inscribed radius / circumscribed radius”, which is a measure that is largely used in the community of simplicial meshes. This form is closely related to the ICN measure.
- For quadrangles and prisms, ‘Gamma’ is computed on the worst corner using the formula [1 - abs(r)] where r is proportional to the difference between the corner angle and the perfect (solid) angle, that is pi/2 for quads and pi/3 for prisms. This form is closely related to the IGE measure.For the exact definitions, see src/geo/MElement.cpp, and, for the ICN and IGE measures, see the paper A. Johnen, C. Geuzaine, T. Toulorge and J.-F. Remacle, “Efficient computation of the minimum of shape quality measures on curvilinear finite elements”, Computer-Aided Design 103, pp. 24-33, 2018.
probably i miss at minIsotropy when reading another paper from the authors, shown have relation to Jacobian determinant.
2 Likes
What are recommended values - ranges for this parameters ?