Mesh Data

Partial Differential Equation Toolbox™ uses meshes with triangular elements for 2-D geometries and meshes with tetrahedral elements for 3-D geometries. In both cases, it uses quadratic elements by default, and provides the option to switch to linear elements. A mesh always consists of elements of the same type. The toolbox does not support mixed meshes.

The triangles in 2-D meshes are specified by three nodes for linear elements or six nodes for quadratic elements. A triangle representing a linear element has nodes at the corners. A triangle representing a quadratic element has nodes at its corners and edge centers.

The tetrahedra in 3-D meshes are specified by four nodes for linear elements or 10 nodes for quadratic elements. A tetrahedron representing a linear element has nodes at the corners. A tetrahedron representing a quadratic element has nodes at its corners and edge centers.

The model container object stores the parameters of the PDE model. The toolbox offers several types of model container objects, each for a particular application area. For example, for linear elasticity problems, the model container is a StructuralModel object, and for heat transfer problems, the model container is a ThermalModel object. For general PDE problems, the toolbox uses the PDEModel object.

The Mesh property of the model container object stores mesh data. The Mesh property contains a FEMesh object. FEMesh Properties include information on the nodes and elements of the mesh, mesh growth rate, and target minimum and maximum element size. The properties also indicate whether the mesh is linear or quadratic. You can specify these mesh parameters when creating a mesh.

To generate a mesh for your PDE model, use the generateMesh function.

By default, generateMesh uses the quadratic geometric order, which typically produces more accurate results than the linear geometric order. To switch to the linear geometric order, call the mesh generator and set the GeometricOrder name-value pair to 'linear'.