meshQuality

Evaluate shape quality of mesh elements

Syntax

Q = meshQuality(mesh)

Q = meshQuality(mesh,elemIDs)

Q = meshQuality(___,'aspect-ratio')

Description

Q = meshQuality(mesh) returns a row vector of numbers from 0 through 1 representing shape quality of all elements of the mesh. Here, 1 corresponds to the optimal shape of the element.

Q = meshQuality(mesh,elemIDs) returns the shape quality of the specified elements.

Q = meshQuality(___,'aspect-ratio') determines the shape quality by using the ratio of minimal to maximal dimensions of an element. The quality values are numbers from 0 through 1, where 1 corresponds to the optimal shape of the element. Specify 'aspect-ratio' after any of the previous syntaxes.

Examples

Element Quality of 3-D Mesh

Evaluate the shape quality of the elements of a 3-D mesh.

Create a PDE model.

model = createpde;

Include and plot the following geometry.

importGeometry(model,'PlateSquareHoleSolid.stl');
pdegplot(model)

Create and plot a coarse mesh.

mesh = generateMesh(model,'Hmax',35)

mesh = 
  FEMesh with properties:

             Nodes: [3x487 double]
          Elements: [10x213 double]
    MaxElementSize: 35
    MinElementSize: 17.5000
     MeshGradation: 1.5000
    GeometricOrder: 'quadratic'

pdemesh(model)

Evaluate the shape quality of all mesh elements. Display the first five values.

Q = meshQuality(mesh);
Q(1:5)

ans = 1×5

    0.3079    0.2917    0.6189    0.6688    0.5571

Find the elements with the quality values less than 0.2.

elemIDs = find(Q < 0.2);

Highlight these elements in blue on the mesh plot.

pdemesh(mesh,'FaceAlpha',0.5)
hold on
pdemesh(mesh.Nodes,mesh.Elements(:,elemIDs),'FaceColor','blue','EdgeColor','blue')

Plot the element quality in a histogram.

figure
hist(Q)
xlabel('Element Shape Quality','fontweight','b')
ylabel('Number of Elements','fontweight','b')

Find the worst quality value.

Qworst = min(Q)

Qworst = 0.1691

Find the corresponding element IDs.

elemIDs = find(Q==Qworst)

elemIDs = 1×2

    10   136

Element Quality of 2-D Mesh

Evaluate the shape quality of the elements of a 2-D mesh.

Create a PDE model.

model = createpde;

Include and plot the following geometry.

importGeometry(model,'PlateSquareHolePlanar.stl');
pdegplot(model)

Create and plot a coarse mesh.

mesh = generateMesh(model,'Hmax',20)

mesh = 
  FEMesh with properties:

             Nodes: [2x286 double]
          Elements: [6x126 double]
    MaxElementSize: 20
    MinElementSize: 10
     MeshGradation: 1.5000
    GeometricOrder: 'quadratic'

pdemesh(model)

Find the IDs of the elements within a box enclosing the center of the plate.

elemIDs = findElements(mesh,'box',[25,75],[80,120]);

Evaluate the shape quality of these elements.

Q = meshQuality(mesh,elemIDs)

Q = 1×12

    0.2980    0.8253    0.2994    0.6581    0.7838    0.6104    0.3992    0.6921    0.2948    0.5726    0.7016    0.5669

Find the elements with the quality values less than 0.4.

elemIDs04 = elemIDs(Q < 0.4)

elemIDs04 = 1×4

     9    19    69    83

Highlight these elements in green on the mesh plot. Zoom in to see the details.

pdemesh(mesh,'ElementLabels','on')
hold on
pdemesh(mesh.Nodes,mesh.Elements(:,elemIDs04),'EdgeColor','green')
zoom(10)

Element Quality Determined by Aspect Ratio

Determine the shape quality of mesh elements by using the ratios of minimal to maximal dimensions.

Create a PDE model and include the L-shaped geometry.

model = createpde(1);
geometryFromEdges(model,@lshapeg);

Generate the default mesh for the geometry.

mesh = generateMesh(model);

View the mesh.

pdeplot(model)

Evaluate the shape quality of mesh elements by using the minimal to maximal dimensions ratio. Display the first five values.

Q = meshQuality(mesh,'aspect-ratio');
Q(1:5)

ans = 1×5

    0.8339    0.7655    0.7755    0.8301    0.8969

Evaluate the shape quality of mesh elements by using the default setting. Display the first five values.

Q = meshQuality(mesh);
Q(1:5)

ans = 1×5

    0.9837    0.9605    0.9654    0.9829    0.9913

Input Arguments

mesh — Mesh object

Mesh property of a PDEModel object | output of generateMesh

Mesh object, specified as the Mesh property of a PDEModel object or as the output of generateMesh.

Example: model.Mesh

elemIDs — Element IDs

positive integer | matrix of positive integers

Element IDs, specified as a positive integer or a matrix of positive integers.

Example: [10 68 81 97 113 130 136 164]

Output Arguments

Q — Shape quality of mesh elements

row vector of numbers from 0 through 1

Shape quality of mesh elements, returned as a row vector of numbers from 0 through 1. The value 0 corresponds to a deflated element with zero area or volume. The value 1 corresponds to an element of optimal shape.

Example: [0.9150 0.7787 0.9417 0.2744 0.9843 0.9181]

Data Types: double

References

[1] Knupp, Patrick M. "Matrix Norms & the Condition Number: A General Framework to Improve Mesh Quality via Node-Movement." In Proceedings, 8th International Meshing Roundtable. Lake Tahoe, CA, October 1999: 13-22.