initmesh
Create initial 2-D mesh
This page describes the legacy workflow. New features might
not be compatible with the legacy workflow. For the corresponding
step in the recommended workflow, see generateMesh.
Syntax
[p,e,t] = initmesh(g) [p,e,t] = initmesh(g,'PropertyName',PropertyValue,...)
Description
[p,e,t] = initmesh(g) returns
a triangular mesh using the 2-D geometry specification g. initmesh uses
a Delaunay triangulation algorithm. The mesh size is determined from
the shape of the geometry and from name-value pair settings.
g describes the geometry of the PDE problem.
g can be a Decomposed Geometry matrix, the name of a Geometry file,
or a function handle to a Geometry file.
The outputs p, e, and t are
the mesh data.
In the Point matrix p,
the first and second rows contain x- and y-coordinates
of the points in the mesh.
In the Edge matrix e,
the first and second rows contain indices of the starting and ending
point, the third and fourth rows contain the starting and ending parameter
values, the fifth row contains the edge segment number, and the sixth
and seventh row contain the left- and right-hand side subdomain numbers.
In the Triangle matrix t,
the first three rows contain indices to the corner points, given in
counter clockwise order, and the fourth row contains the subdomain
number.
initmesh accepts the following name/value
pairs.
| Name | Value | Default | Description |
|---|---|---|---|
Hmax | numeric | estimate | Maximum edge size |
Hgrad | numeric, strictly between | 1.3 | Mesh growth rate |
Box |
| 'off' | Preserve bounding box |
Init |
| 'off' | Edge triangulation |
Jiggle |
|
| Call jigglemesh after creating
the mesh, with the Opt name-value pair set to the
stated value. Exceptions: 'off' means do not call jigglemesh,
and 'on' means call jigglemesh with Opt = 'off'. |
JiggleIter | numeric | 10 | Maximum iterations |
MesherVersion |
| 'preR2013a' | Algorithm for generating initial mesh |
The Hmax property controls the size of the
triangles on the mesh. initmesh creates a mesh
where triangle edge lengths are approximately Hmax or
less.
The Hgrad property determines the mesh growth
rate away from a small part of the geometry. The default value is 1.3,
i.e., a growth rate of 30%. Hgrad cannot be equal
to either of its bounds, 1 and 2.
Both the Box and Init property
are related to the way the mesh algorithm works. By turning on Box you
can get a good idea of how the mesh generation algorithm works within
the bounding box. By turning on Init you can see
the initial triangulation of the boundaries. By using the command
sequence
[p,e,t] = initmesh(dl,'hmax',inf,'init','on'); [uxy,tn,a2,a3] = tri2grid(p,t,zeros(size(p,2)),x,y); n = t(4,tn);
you can determine the subdomain number n of
the point xy. If the point is outside the geometry, tn is NaN and
the command n = t(4,tn) results in a failure.
The Jiggle property is used to control whether
jiggling of the mesh should be attempted (see jigglemesh for
details). Jiggling can be done until the minimum or the mean of the
quality of the triangles decreases. JiggleIter can
be used to set an upper limit on the number of iterations.
The MesherVersion property chooses the algorithm
for mesh generation. The 'R2013a' algorithm runs
faster, and can triangulate more geometries than the 'preR2013a' algorithm.
Both algorithms use Delaunay triangulation.
Examples
Make a simple triangular mesh of the L-shaped membrane in the PDE Modeler app. Before you do
anything in the PDE Modeler app, set the Maximum edge size to
inf in the Mesh Parameters dialog box. You open the dialog box by
selecting the Parameters option from the
Mesh menu. Also select the items Show Node
Labels and Show Triangle Labels in the
Mesh menu. Then create the initial mesh by pressing the button. (This can also be done by selecting the
Initialize
Mesh option from the Mesh
menu.)
The following figure appears.
The corresponding mesh data structures can be exported to the main workspace by selecting the Export Mesh option from the Mesh menu.
p p = -1 1 1 0 0 -1 -1 -1 1 1 0 0 e e = 1 2 3 4 5 6 2 3 4 5 6 1 0 0 0 0 0 0 1 1 1 1 1 1 1 2 3 4 5 6 1 1 1 1 1 1 0 0 0 0 0 0 t t = 1 2 3 1 2 3 4 5 5 5 5 6 1 1 1 1
References
George, P. L., Automatic Mesh Generation — Application to Finite Element Methods, Wiley, 1991.