GridStatistics

Type:section Appearance:simple Excludes:CartesianToFourierTransform, ConvertToPowerFlux, CreateReducedBasis, DensityIntegration, DipoleEmission, EvaluateReducedBasis, ExportFields, ExportGrid, FarField, FluxIntegration, FourierTransform, IntegrationWeights, LayeredMediaSolver, ModeOverlap, MultipoleExpansion, OpticalImaging, PupilField, Radiation, ResonanceExpansion, ResonanceOverlap, ScatteringMatrix, Superposition, SurfaceDensityIntegration

This PostProcess exports statistics of the mesh given by InputFileName. The export contains three tables reporting different statistics:

• The first table contains basic statistics (minimum, maximum, average and median) about domain and element volumes (or areas in 2D). It also gives an indication of the geometrical mesh quality described by quantities below. For a detailed discussion of advantages of the different measures see [1]. These exported quality measures include

  • EdgeLength - the edge lengths ,
  • EdgeRatio - the ratio of the longest edge to the smallest in each element, i.e. ,
  • InnerAngle - the inner angle of triangles,
  • Q1 - ,
  • Q2 - ,
  • Q3 - which is the inverse of the commonly used aspect ratio,
  • Q5 - ,
  • AreaRatio - the ratio of the areas of the largest and smallest facets in each element (only in 3D),
  • DihedralAngle - the dihedral angle of tetrahedrons (only in 3D),

  where are the minimum and maximum edge lengths of the element with volume in dimension and are the insphere and circumsphere radii of the elements.

  Furthermore this table lists the CenterOfGravity and the moment of inertia tensor InertiaTensor for every domain.

• The second table contains more detailed distributions of the same quantities. You can use a bar plot function to plot them directly. The header includes the DomainId stored with the same index as the densities.

• The third table lists the area (or length for the 2D case) of the interfaces between domains.

Storage format

GridStatistics appends three JCM tables to its output file :

1. The first table is Volumes in 3-D or Areas in 2-D. It has one row per selected physical domain. Its columns are named:
   • DomainId;
   • Volume or Area;
   • SmallestElement<Volume|Area>, LargestElement<Volume|Area>, AverageElement<Volume|Area>, MedianElement<Volume|Area>;
   • for each criterion EdgeLength, InnerAngle, EdgeRatio, Q1, Q2, Q3, Q5 and, in 3-D, AreaRatio and DihedralAngle: Smallest<Criterion>, Largest<Criterion>, Average<Criterion>, Median<Criterion>;
   • CenterOfGravityX, CenterOfGravityY, CenterOfGravityZ; and
   • InertiaTensor_1_1 through InertiaTensor_3_3.
2. The second table is VolumeHistograms in 3-D or AreaHistograms in 2-D. It stores histogram bins in parallel column pairs LowerBound<Quantity>_<i>, Value<Quantity>_<i>. The metadata entry DomainId_<i> identifies the domain belonging to each pair. Row j is bin j of every populated histogram; absent bins are represented by NaN.
3. The third table is DomainInterfaceArea in 3-D or DomainInterfaceLength in 2-D. Each row is an oriented domain pair. Its columns are named:
   • DomainIdFirst, DomainIdSecond, DomainInterfaceArea or DomainInterfaceLength.

[1]	http://www.iue.tuwien.ac.at/phd/fleischmann/node13.html