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: [3x854 double]
          Elements: [10x378 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

    0.6533    0.6640    0.7480    0.7721    0.8736

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 = 0.1867

Find the corresponding element IDs.

elemIDs = find(Q==Qworst)

elemIDs = 377

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: [2x298 double]
          Elements: [6x132 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. Display the result as a column vector.

Q = meshQuality(mesh,elemIDs);
Q.'

ans = 16×1

    0.3623
    0.9973
    0.6361
    0.3497
    0.7660
    0.7858
    0.9843
    0.7858
    0.3439
    0.3623
      ⋮

Find the elements with the quality values less than 0.4.

elemIDs04 = elemIDs(Q < 0.4)

elemIDs04 = 1×4

     5    26    47    51

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

    0.8102    0.8721    0.9964    0.8141    0.9964

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

    0.9727    0.9903    1.0000    0.9740    1.0000