Geometry from Triangulated Mesh

3-D Geometry from Finite Element Mesh

This example shows how to create an fegeometry object and a DiscreteGeometry object from a 3-D mesh.

The tetmesh file, which is included in Partial Differential Equation Toolbox™, contains a 3-D tetrahedral mesh. Load the data into your workspace.

load tetmesh

The imported variable tet contains a connectivity list, and the variable X contains a matrix of points. Using these variables, create the triangulation representation.

TR = triangulation(tet,X)

TR = 
  triangulation with properties:

              Points: [1456x3 double]
    ConnectivityList: [4969x4 double]

Create an fegeometry object from the triangulation object.

gm = fegeometry(TR)

gm = 
  fegeometry with properties:

       NumCells: 1
       NumFaces: 23
       NumEdges: 50
    NumVertices: 30
       Vertices: [30x3 double]
           Mesh: [1x1 FEMesh]

The geometry contains the imported linear mesh.

gm.Mesh

ans = 
  FEMesh with properties:

             Nodes: [3x1456 double]
          Elements: [4x4969 double]
    MaxElementSize: 8.2971
    MinElementSize: 1.9044
     MeshGradation: []
    GeometricOrder: 'linear'

To create a more accurate quadratic mesh, use generateMesh.

gm = generateMesh(gm);
gm.Mesh

ans = 
  FEMesh with properties:

             Nodes: [3x9380 double]
          Elements: [10x4732 double]
    MaxElementSize: 4.9820
    MinElementSize: 2.4910
     MeshGradation: 1.5000
    GeometricOrder: 'quadratic'

Plot the geometry with the face labels.

pdegplot(gm,FaceLabels="on",FaceAlpha=0.5);

Alternatively, you can create a geometry as a DiscreteGeometry object. First, create data matrices of the appropriate sizes.

nodes = X';
elements = tet';

Then, create a PDE model and use geometryFromMesh to create a geometry from the mesh.

model = createpde;
gm = geometryFromMesh(model,nodes,elements)

gm = 
  DiscreteGeometry with properties:

       NumCells: 1
       NumFaces: 23
       NumEdges: 50
    NumVertices: 30
       Vertices: [30x3 double]

The model contains the imported linear mesh.

model.Mesh

ans = 
  FEMesh with properties:

             Nodes: [3x1456 double]
          Elements: [4x4969 double]
    MaxElementSize: 8.2971
    MinElementSize: 1.9044
     MeshGradation: []
    GeometricOrder: 'linear'

To create a more accurate quadratic mesh, use generateMesh.

generateMesh(model)

ans = 
  FEMesh with properties:

             Nodes: [3x9380 double]
          Elements: [10x4732 double]
    MaxElementSize: 4.9820
    MinElementSize: 2.4910
     MeshGradation: 1.5000
    GeometricOrder: 'quadratic'

2-D Multidomain Geometry

Create a 2-D multidomain geometry from a planar mesh.

The MultidomainMesh2D file, which is included in Partial Differential Equation Toolbox™, contains a 2-D mesh. Load information about nodes, elements, and element-to-domain correspondence into your workspace.

load MultidomainMesh2D

Create a geometry from the mesh nodes and elements.

gm = fegeometry(nodes',elements',ElementIdToRegionId);

Plot the geometry with the face labels.

pdegplot(gm,FaceLabels="on")