CIBC:Documentation:SCIRun:Reference:SCIRun:ReportMeshQualityMeasures
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ReportMeshQualityMeasures
Information
- Package: SCIRun
- Catagory: ChangeFieldData
- Author(s): Jason Shepherd
- Status: Supported in latest version
- Version: 3.0
Description
Summary
Nodal movement to improve mesh quality.
Detailed Description
The ReportMeshQualityMeasures module is used to calculate multiple mesh quality metrics and report these metrics to the user. The Sandia National Laboratories VERDICT library (http://cubit.sandia.gov/verdict.html) performs the metric calculations.
Metric descriptions are taken from VERDICT as follows (descriptions are by element type.)
Description of Tetrahedral Quality Measures
Function Name Dimension Full Range Acceptable Range Reference ------------- ---------- -------- --------------- --------- Aspect Ratio Bet L^0 1 to inf 1 to 3 1 Aspect Ratio Gam L^0 1 to inf 1 to 3 1 Element Volume L^3 -inf to +inf None 1 Condition No. L^0 1 to inf 1 to 3 2 Jacobian L^3 -inf to inf None 2 Scaled Jacobian L^0 -1.414 to +1.414 0.5 to +1.414 2 Shape L^0 0 to 1 0.2 to 1 3 Relative Size L^0 0 to 1 0.2 to 1 3 Shape and Size L^0 0 to 1 0.2 to 1 3 Distortion L^2 -1 to 1 0.6 to 1 4 ------------- ---------- -------- -------------- ---------
Approximate Tetrahedral Quality Definitions: Aspect Ratio Beta: CR / (3.0 * IR) where CR = circumsphere radius, IR = inscribed sphere radius Aspect Ratio Gamma: Srms**3 / (8.479670*V) where Srms = sqrt(Sum(Si**2)/6), Si = edge length Element Volume: (1/6) * Jacobian at corner node Condition No. Condition number of the Jacobian matrix at any corner Jacobian: Minimum pointwise volume at any corner Scaled Jacobian: Minimum Jacobian divided by the lengths of 3 edge vectors Shape: 3/Mean Ratio of weighted Jacobian matrix Relative Size: Min( J, 1/J ), where J is determinant of weighted Jacobian matrix Shape and Size: Product of Shape and Relative Size Distortion: {min(|J|)/actual volume}*parent volume, parent volume = 1/6 for tet
References for Tetrahedral Quality Measures: 1. V. N. Parthasarathy et al, A comparison of tetrahedron quality measures, Finite Elem. Anal. Des., Vol 15(1993), 255-261. 2. P. Knupp, Achieving Finite Element Mesh Quality via Optimization of the Jacobian Matrix Norm and Associated Quantities, Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. 3. P. Knupp, Algebraic Mesh Quality Metrics for Unstructured Initial Meshes, submitted for publication. 4. SDRC/IDEAS Simulation: Finite Element Modeling--User's Guide
Description of Hexahedral Quality Measures
Function Name Dimension Full Range Acceptable Range Reference ------------- ---------- ----- --------------- --------- Aspect Ratio L^0 1 to inf 1 to 4 1 Skew L^0 0 to 1 0 to 0.5 1 Taper L^0 0 to +inf 0 to 0.4 1 Element Volume L^3 -inf to +inf None 1 Stretch L^0 0 to 1 0.25 to 1 2 Diagonal Ratio L^0 0 to 1 0.65 to 1 3 Dimension L^1 0 to inf None 1 Condition No. L^0 1 to inf 1 to 8 4 Jacobian L^3 - inf to inf None 4 Scaled Jacobian L^0 -1 to +1 0.5 to 1 4 Shear L^0 0 to 1 0.3 to 1 5 Shape L^0 0 to 1 0.3 to 1 5 Relative Size L^0 0 to 1 0.5 to 1 5 Shear and Size L^0 0 to 1 0.2 to 1 5 Shape and Size L^0 0 to 1 0.2 to 1 5 Distortion L^2 -1 to 1 0.6 to 1 6 ------------- ---------- ----- ---------------- ---------
Approximate Hexahedral Quality Definitions: Aspect Ratio: Maximum edge length ratios at hex center. Skew: Maximum |cos A| where A is the angle between edges at hex center. Taper: Maximum ratio of lengths derived from opposite edges. Element Volume: Jacobian at hex center. Stretch: Sqrt(3) * minimum edge length / maximum diagonal length. Diagonal Ratio: Minimum diagonal length / maximum diagonal length. Dimension: Pronto-specific characteristic length for stable time step calculation. Char_length = Volume / 2 grad Volume. Condition No. Maximum condition number of the Jacobian matrix at 8 corners. Jacobian: Minimum pointwise volume of local map at 8 corners and center of hex. Scaled Jacobian: Minimum Jacobian divided by the lengths of the 3 edge vectors. Shear: 3/Mean Ratio of Jacobian Skew matrix Shape: 3/Mean Ratio of weighted Jacobian matrix Relative Size: Min( J, 1/J ), where J is determinant of weighted Jacobian matrix Shear and Size: Product of Shear and Relative Size Shape and Size: Product of Shape and Relative Size Distortion: {min(|J|)/actual volume}*parent volume, parent volume = 8 for hex
References for Hexahedral Quality Measures: 1. L.M. Taylor, and D.P. Flanagan, Pronto3D - A Three Dimensional Transient Solid Dynamics Program, SAND87-1912, Sandia National Laboratories, 1989. 2. FIMESH code 3. Unknown 4. P. Knupp, Achieving Finite Element Mesh Quality via Optimization of the Jacobian Matrix Norm and Associated Quantities, Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. 5. P. Knupp, Algebraic Mesh Quality Metrics for Unstructured Initial Meshes, submitted for publication. 6. SDRC/IDEAS Simulation: Finite Element Modeling--User's Guide
Description of Triangular Quality Measures
Function Name Dimension Full Range Acceptable Range Reference ------------- ---------- --------- --------------- --------- Element Area L^2 0 to inf None 1 Maximum Angle degrees 60 to 180 60 to 90 1 Minimum Angle degrees 0 to 60 30 to 60 1 Condition No. L^0 1 to inf 1 to 1.3 2 Scaled Jacobian L^0 -1.155 to +1.155 0.5 to 1.155 2 Relative Size L^0 0 to 1 0.25 to 1 3 Shape L^0 0 to 1 0.25 to 1 3 Shape and Size L^0 0 to 1 0.25 to 1 3 Distortion L^2 -1 to 1 0.6 to 1 4 ------------- ---------- -------- --------------- ---------
Approximate Triangular Quality Definitions: Element Area: (1/2) * Jacobian at corner node Maximum Angle: Maximum included angle in triangle Minimum Angle: Minimum included angle in triangle Condition No. Condition number of the Jacobian matrix Scaled Jacobian: Minimum Jacobian divided by the lengths of 2 edge vectors Relative Size: Min( J, 1/J ), where J is determinant of weighted Jacobian matrix Shape: 2/Condition number of weighted Jacobian matrix Shape and Size: Product of Shape and Relative Size Distortion: {min(|J|)/actual area}*parent area, parent area = 1/2 for triangular element
References for Triangular Quality Measures: 1. Traditional. 2. P. Knupp, Achieving Finite Element Mesh Quality via Optimization of the Jacobian Matrix Norm and Associated Quantities, Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. 3. P. Knupp, Algebraic Mesh Quality Metrics for Unstructured Initial Meshes, submitted for publication. 4. SDRC/IDEAS Simulation: Finite Element Modeling--User's Guide
Description of Quadrilateral Quality Measures
Function Name Dimension Full Range Acceptable Range Reference ------------- ---------- ----- --------------- --------- Aspect Ratio L^0 1 to inf 1 to 4 1 Skew L^0 0 to 1 0 to 0.5 1 Taper L^0 0 to inf 0 to 0.7 1 Warpage L^0 0 to 1 0.9 to 1.0 1 Element Area L^2 -inf to +inf None 1 Stretch L^0 0 to 1 0.25 to 1 2 Minimum Angle degrees 0 to 90 45 to 90 3 Maximum Angle degrees 90 to 360 90 to 135 3 Condition No. L^0 1 to inf 1 to 4 4 Jacobian L^2 - inf to inf None 4 Scaled Jacobian L^0 -1 to +1 0.5 to 1 4 Shear L^0 0 to 1 0.3 to 1 5 Shape L^0 0 to 1 0.3 to 1 5 Relative Size L^0 0 to 1 0.3 to 1 5 Shear and Size L^0 0 to 1 0.2 to 1 5 Shape and Size L^0 0 to 1 0.2 to 1 5 Distortion L^2 -1 to 1 0.6 to 1 6 ------------- ---------- ----- -------------- ---------
Approximate Quadrilateral Quality Definitions: Aspect Ratio: Maximum edge length ratios at quad center Skew: Maximum |cos A| where A is the angle between edges at quad center Taper: Maximum ratio of lengths derived from opposite edges Warpage: Cosine of Minimum Dihedral Angle formed by Planes Intersecting in Diagonals Element Area: Jacobian at quad center Stretch: Sqrt(2) * minimum edge length / maximum diagonal length Minimum Angle: Smallest included quad angle (degrees). Maximum Angle: Largest included quad angle (degrees). Condition No. Maximum condition number of the Jacobian matrix at 4 corners Jacobian: Minimum pointwise volume of local map at 4 corners and center of quad Scaled Jacobian: Minimum Jacobian divided by the lengths of the 2 edge vectors Shear: 2/Condition number of Jacobian Skew matrix Shape: 2/Condition number of weighted Jacobian matrix Relative Size: Min( J, 1/J ), where J is determinant of weighted Jacobian matrix Shear and Size: Product of Shear and Relative Size Shape and Size: Product of Shape and Relative Size Distortion: {min(|J|)/actual area}*parent area, parent area = 4 for quad
References for Quadrilateral Quality Measures: 1. J. Robinson, CRE Method of element testing and the Jacobian shape parameters, Eng. Comput., Vol 4, 1987. 2. FIMESH code. 3. Unknown. 4. P. Knupp, Achieving Finite Element Mesh Quality via Optimization of the Jacobian Matrix Norm and Associated Quantities, Intl. J. Numer. Meth. Engng. 2000, 48:1165-1185. 5. P. Knupp, Algebraic Mesh Quality Metrics for Unstructured Initial Meshes, submitted for publication. 6. SDRC/IDEAS Simulation: Finite Element Modeling--User's Guide
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