Create initial 2D mesh
THIS PAGE DESCRIBES
THE LEGACY APPROACH. New features might not be
compatible with the legacy workflow. For the corresponding step in
the recommended workflow, see generateMesh
.
[p,e,t] = initmesh(g) [p,e,t] = initmesh(g,'PropertyName',PropertyValue,...)
[p,e,t] = initmesh(g)
returns
a triangular mesh using the 2D geometry specification g
. initmesh
uses
a Delaunay triangulation algorithm. The mesh size is determined from
the shape of the geometry and from namevalue 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. For details, see 2D Geometry.
The outputs p
, e
, and t
are
the mesh data.
In the Point matrix p
,
the first and second rows contain x and ycoordinates
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 righthand 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 namevalue 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.
Make a simple triangular mesh of the Lshaped membrane in the
PDE app. Before you do anything in the PDE 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 $$\Delta $$ 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
George, P. L., Automatic Mesh Generation — Application to Finite Element Methods, Wiley, 1991.