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

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)

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