generateMesh

Create triangular or tetrahedral mesh

Syntax

generateMesh(model)

generateMesh(model,Name,Value)

mesh = generateMesh(___)

Description

generateMesh(model) creates a mesh and stores it in the model object. model must contain a geometry. To include 2-D geometry in a model, use geometryFromEdges. To include 3-D geometry, use importGeometry or geometryFromMesh.

generateMesh can return slightly different meshes in different releases. For example, the number of elements in the mesh can change. Avoid writing code that relies on explicitly specified node and element IDs.

generateMesh(model,Name,Value) modifies the mesh creation according to the Name,Value arguments.

mesh = generateMesh(___) also returns the mesh to the MATLAB^® workspace, using any of the previous syntaxes.

Examples

Generate 2-D Mesh

Generate the default 2-D mesh for the L-shaped geometry.

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

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

Generate the default mesh for the geometry.

generateMesh(model);

View the mesh.

pdeplot(model)

Generate 3-D Mesh

Create a mesh that is finer than the default.

Create a PDE model and include the BracketTwoHoles geometry.

model = createpde(1);
importGeometry(model,'BracketTwoHoles.stl');

Generate a default mesh for comparison.

generateMesh(model)

ans = 
  FEMesh with properties:

             Nodes: [3x10003 double]
          Elements: [10x5774 double]
    MaxElementSize: 9.7980
    MinElementSize: 4.8990
     MeshGradation: 1.5000
    GeometricOrder: 'quadratic'

View the mesh.

pdeplot3D(model)

Create a mesh with target maximum element size 5 instead of the default 7.3485.

generateMesh(model,'Hmax',5)

ans = 
  FEMesh with properties:

             Nodes: [3x66982 double]
          Elements: [10x44093 double]
    MaxElementSize: 5
    MinElementSize: 2.5000
     MeshGradation: 1.5000
    GeometricOrder: 'quadratic'

View the mesh.

pdeplot3D(model)

Input Arguments

model — Model object

PDEModel object | ThermalModel object | StructuralModel object | ElectromagneticModel object

Model object, specified as a PDEModel object, ThermalModel object, StructuralModel object, or ElectromagneticModel object.

Example: model = createpde(3)

Example: thermalmodel = createpde('thermal','steadystate')

Example: structuralmodel = createpde('structural','static-solid')

Example: emagmodel = createpde('electromagnetic','electrostatic')

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: generateMesh(model,'Hmax',0.25);

'GeometricOrder' — Element geometric order

'quadratic' (default) | 'linear'

Element geometric order, specified as the comma-separated pair consisting of 'GeometricOrder' and 'linear' or 'quadratic'.

A triangle or tetrahedron representing a linear element has nodes at the corners. A triangle or tetrahedron representing a quadratic element has nodes at its corners and edge centers. The center nodes in quadratic meshes are always added at half-distance between corners. For geometries with curved surfaces and edges, center nodes might not appear on the edge or surface itself.

In general, 'quadratic' elements produce more accurate solutions. Override the default 'quadratic' only to save memory or to solve a 2-D problem using a legacy solver. Legacy PDE solvers use linear triangular mesh for 2-D geometries.

Example: generateMesh(model,'GeometricOrder','linear');

Data Types: char | string

'Hgrad' — Mesh growth rate

1.5 (default) | number greater than or equal to 1 and less than or equal to 2

Mesh growth rate, specified as the comma-separated pair consisting of Hgrad and a number greater than or equal to 1 and less than or equal to 2.

Example: generateMesh(model,'Hgrad',1.3);

Data Types: double

'Hmax' — Target maximum mesh edge length

positive real number

Target maximum mesh edge length, specified as the comma-separated pair consisting of Hmax and a positive real number.

Hmax is an approximate upper bound on the mesh edge lengths. Occasionally, generateMesh can create a mesh with some elements that exceed Hmax.

generateMesh estimates the default value of Hmax from overall dimensions of the geometry.

Small Hmax values let you create finer meshes, but mesh generation can take a very long time in this case. You can interrupt mesh generation by using Ctrl+C. Note that generateMesh can take additional time to respond to the interrupt.

Example: generateMesh(model,'Hmax',0.25);

Data Types: double

'Hmin' — Target minimum mesh edge length

nonnegative real number

Target minimum mesh edge length, specified as the comma-separated pair consisting of Hmin and a nonnegative real number.

Hmin is an approximate lower bound on the mesh edge lengths. Occasionally, generateMesh can create a mesh with some elements that are smaller than Hmin.

generateMesh estimates the default value of Hmin from overall dimensions of the geometry.

Example: generateMesh(model,'Hmin',0.05);

Data Types: double

Output Arguments

mesh — Mesh description

FEMesh object

Mesh description, returned as an FEMesh Properties object. mesh is the same as model.Mesh.

More About

Element

An element is a basic unit in the finite-element method.

For 2-D problems, an element is a triangle in the model.Mesh.Element property. If the triangle represents a linear element, it has nodes only at the triangle corners. If the triangle represents a quadratic element, then it has nodes at the triangle corners and edge centers.

For 3-D problems, an element is a tetrahedron with either four or ten points. A four-point (linear) tetrahedron has nodes only at its corners. A ten-point (quadratic) tetrahedron has nodes at its corners and at the center point of each edge.

For details, see Mesh Data.