initmesh

R2026b

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,Name=Value)

Description

[p,e,t] = initmesh(g) generates a triangular mesh for a 2-D geometry. The function uses a Delaunay triangulation algorithm.

[p,e,t] = initmesh(g,Name=Value) generates a 2-D mesh using one or more Name=Value pair arguments.

Examples

Initial Mesh for L-shaped Membrane

Generate a triangular mesh of the L-shaped membrane.

[p,e,t] = initmesh("lshapeg");

Plot the mesh.

pdemesh(p,e,t)

Maximum Mesh Edge Length

Generate a triangular mesh of the L-shaped membrane with the target maximum mesh edge length of 0.1.

[p,e,t] = initmesh("lshapeg",Hmax=0.1);

Plot the mesh.

pdemesh(p,e,t)

Input Arguments

g — Geometry description

decomposed geometry matrix | geometry function | handle to geometry function

Geometry description, specified as a decomposed geometry matrix, a geometry function, or a handle to the geometry function. For details about a decomposed geometry matrix, see decsg. For details about a geometry function, see Parameterized Function for 2-D Geometry Creation.

A geometry function must return the same result for the same input arguments in every function call. Thus, it must not contain functions and expressions designed to return a variety of results, such as random number generators.

Data Types: double | char | string | function_handle

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: [p,e,t] = initmesh("lshapeg",Hmax=0.1);

Hmax — Target maximum mesh edge length

positive real number

Target maximum mesh edge length, specified as a positive real number.

Hmax is an approximate upper bound on the mesh edge lengths. initmesh 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 initmesh can take additional time to respond to the interrupt.

Example: [p,e,t] = initmesh(g,Hmax=0.25);

Data Types: double

Hgrad — Mesh growth rate

1.3 (default) | number strictly greater than 1 and less than 2

Mesh growth rate, specified as a number strictly greater than 1 and less than 2.

Example: [p,e,t] = initmesh(g,Hgrad=1.5);

Data Types: double

Box — Toggle to preserve bounding box

"off" (default) | "on"

Toggle to preserve bounding box, specified as "on" or "off". By turning on "Box" you can get a good idea of how the mesh generation algorithm works within the bounding box.

Example: [p,e,t] = initmesh(g,Box="on");

Data Types: char | string

Init — Toggle to use edge triangulation

"off" (default) | "on"

Toggle to use edge triangulation, specified as "on" or "off". By turning on Init you can see the initial triangulation of the boundaries. For example, use these commands to determine the subdomain number n of the point xy.

[p,e,t] = initmesh(g,Hmax=Inf,Init=,"on"); 
[uxy,tn,a2,a3] = tri2grid(p,t,zeros(size(p,2)),x,y); 
n = t(4,tn); 

If the point is outside the geometry, tn is NaN, and the command n = t(4,tn) results in a failure.

Data Types: char | string

Jiggle — Toggle to call jigglemesh after creating the mesh

"mean" (default) | "minimum" | "on" | "off"

Toggle to call jigglemesh after creating the mesh, specified as "mean", "minimum", "on", or "off".

• "mean" — call jigglemesh with the argument "Opt" set to "mean".

• "minimum" — call jigglemesh with the argument "Opt" set to "minimum".

• "on" — call jigglemesh with the argument "Opt" set to "off".

• "off" — do not call jigglemesh.

Example: [p,e,t] = initmesh(g,Jiggle="minimum");

Data Types: char | string

JiggleIter — Maximum number of iterations for jigglemesh

10 (default) | positive integer

Maximum number of iterations for jigglemesh, specified as a positive integer.

Example: [p,e,t] = initmesh(g,Jiggle="on",JiggleIter=50);

Data Types: double

MesherVersion — Algorithm for generating initial mesh

"preR2013a" (default) | "R2013a"

Algorithm for generating initial mesh, specified as "R2013a" or "preR2013a". The "R2013a" algorithm runs faster, and can triangulate more geometries than the "preR2013a" algorithm. Both algorithms use Delaunay triangulation.

Data Types: char | string

Output Arguments

p — Mesh points

2-by-Np matrix

Mesh points, returned as a 2-by-Np matrix. Np is the number of points (nodes) in the mesh. Column k of p consists of the x-coordinate of point k in p(1,k) and the y-coordinate of point k in p(2,k). For details, see Mesh Data as [p,e,t] Triples.

e — Mesh edges

7-by-Ne matrix

Mesh edges, returned as a 7-by-Ne matrix, where Ne is the number of boundary edges in the mesh. An edge is a pair of points in p containing a boundary between subdomains, or containing an outer boundary. For details, see Mesh Data as [p,e,t] Triples.

t — Mesh elements

4-by-Nt matrix

Mesh elements, returned as a 4-by-Nt matrix. Nt is the number of triangles in the mesh.

The t(i,k), with i ranging from 1 through end - 1, contain indices to the corner points of element k. For details, see Mesh Data as [p,e,t] Triples. The last row, t(end,k), contains the subdomain number of the element.

References

[1] George, P. L. Automatic Mesh Generation — Application to Finite Element Methods. Wiley, 1991.

Version History

Introduced before R2006a

R2013a: Performance and robustness enhancements in meshing algorithm

initmesh provides an enhancement option for increased meshing speed and robustness. Choose the enhanced algorithm by setting the MesherVersion name-value pair to "R2013a". The default MesherVersion value of "preR2013a" gives the same mesh as previous toolbox versions.

The enhancement is available inpdeModeler from the Mesh > Parameters > Mesher version menu.