# Full GUI and CLI Gmsh Mesh Generator Integration with FEATool

# FEATool-Gmsh Mesh Generator Integration

FEATool Multiphysics features full integration with the
*Gmsh* finite element mesh and
grid generator [1][2]. Both 2D and 3D MATLAB
command line interface (CLI) usage is supported with the
gridgen_gmsh function, as well as the
FEATool GUI operation in *grid mode*.

Advantages of using *Gmsh* compared to the built-in (*DistMesh* based)
grid generation function is robustness and mesh generation speed
(primarily for 3D geometries). Moreover, *Gmsh* also supports better
and more control with a selection of different mesh generation
algorithms, and specifying the grid size in different geometry
regions, subdomains, as well as on boundaries, allowing for greater
flexibility and better grids tuned for the specific problems and
geometries. In addition Gmsh also supports generating unstructured 2D
quadrilateral grids automatically.

The gridgen_gmsh function converts
FEATool geometries to Gmsh *geo* data file format, calls *Gmsh* in
non-interactive mode to generate a corresponding finite element FEM
mesh, and parses and imports it back into FEATool. For reference, as
has been introduced previously Gmsh can also be used to
mesh and import CAD geometries to be used with FEATool.

## Installation

First ensure that the latest FEATool Multiphysics version (currently
1.7.1) is installed with either MATLAB. If *Gmsh* has been
selected but not found, FEATool will try to download, and install the
mesh generator binary into the *lib/gmsh* folder of the main FEATool
installation folder.

Should the *Gmsh* installation fail, please manually download and
install *Gmsh* from the original source reference [1].

## GUI Usage

Once installed, the *Grid Generation Settings* dialog box will in 2D
and 3D feature a *Gmsh* selection option from the **Grid Generation
Algorithm** drop-down box. Moreover, the following options also apply
to the *Gmsh* mesh generation algorithm

The

**Subdomain Grid Size**,*hmax*, indicates the target grid cell diameter, and can either be a single scalar prescribing the grid size for the entire geometry, or a space separated string of numbers (array) where the*hmax*values correspond to the generated subdomains.**Boundary Grid Size**,*hmaxb*, is analogous to*hmax*but related to boundaries (edges).*hmaxb*can consist of a single scalar applicable to all boundaries, for example`0.1`

prescribing a mean cell edge length of

*0.1*on every boundary.*hmaxb*can also be a numeric array with entries corresponding to individual boundaries, for example`[ 0.1 0.2 0.3 0.4 ]`

specifying cell edge length

*0.1*for boundary 1,*0.2*for boundary 2 etc.The

**Smoothing**parameter specifies the number of post grid smoothing steps to perform (default 3).In 2D one can also choose between

*Triangular*and*Quadrilateral***Cell Types**.

The **Generate** grid button effectively calls the
gridgen_gmsh function, and in turn
*Gmsh* from the GUI, after which the generated grid is automatically
imported and displayed.

## CLI Usage

On the MATLAB command line the
gridgen_gmsh function is used to call
*Gmsh* to generate an unstructured 2D or 3D triangular grid. The
following syntax is used (analogous to the regular
gridgen function)

```
grid = gridgen_gmsh( SIN, VARARGIN )
```

where SIN is a valid FEATool fea problem struct, geometry struct, or
cell array of geometry
objects. gridgen_gmsh also accepts the
following property/value pairs (*VARARGIN*).

```
Property Value/{Default} Description
-----------------------------------------------------------------------------------
hmax scal/arr {0.1} Target grid size for geometry/subdomains
hmaxb scal/arr {[]} Target grid size for boundaries
nsm scalar {3} Number of grid smoothing steps
nref scalar {0} Number of uniform grid refinements
algo2 scalar {2} 2D mesh algorithm (1=MeshAdapt, 2=Automatic,
5=Delaunay, 6=Frontal, 7=BAMG, 8=DelQuad)
algo3 scalar {1} 3D mesh algorithm (1=Del, 2=New Del, 4=Front
5=Front Del, 6=Front Hex, 7=MMG3D, 9=R-tree)
quad boolean {false} Use quad meshing (for 2D)
mshopt cell {} Cell array of Gmsh options
syscmd string {'default'} Gmsh system call command
(default 'gmsh fdir/fname.geo -')
fname string {'fea_gmsh_UID'} Gmsh imp/exp file name (root)
fdir string {tempdir} Directory to write help files
clean boolean {true} Delete (clean) Gmsh help files
instdir string {'lib/gmsh'} Gmsh binary installation directory
```

Among the properties *hmax* indicates target grid cell diameters, and
is either a numeric scalar valid for the entire geometry or an array
with *hmax* values corresponding to the subdomains. *hmaxb* is similar
to *hmax* but a numeric array with a *hmaxb* values corresponding to
the boundaries (including internal boundaries).

NSM (default 3) the number of post smoothing steps to perform. NREF (default 0) the number of post uniform grid refinement steps. ALGO2 and ALGO3 the Gmsh 2D and 3D mesh generation algorithms. QUAD (default 0) toggles Blossom-Quad conversion for 2D geometries.

Additional Gmsh options can be provided with the cell array MSHOPT.
For example MSHOPT could be given as ```
{{‘Mesh’,
‘CharacteristicLengthMax’, ‘1’}, {‘Mesh’, ‘AnisoMax’, ‘10’}}
```

More detailed information regarding the mesh generation options can be
found in the documentation for *Gmsh* [1]. Also, for more
information about CLI usage access the function help by entering

```
>> help gridgen_gmsh
```

in the MATLAB command line interface.

### Grid Generation Examples

Unit square with uniform global grid size set to

*0.1*.`grid = gridgen_gmsh( {gobj_rectangle()}, 'hmax', 0.1 ); plotgrid( grid )`

Unit square with fine grid along the top boundary.

`grid = gridgen_gmsh( {gobj_rectangle()}, 'hmax', 0.5, ... 'hmaxb', [0.5 0.5 0.01 0.5] ); plotgrid( grid )`

Domain with curved boundaries meshed with quadrilaterals.

`geom.objects = {gobj_rectangle() gobj_circle([0 0],.6) gobj_circle([1 1],.3,'C2')}; geom = geom_apply_formula( geom, 'R1-C1-C2' ); grid = gridgen_gmsh( geom, 'hmax', 0.1, 'quad', true ); plotgrid( grid )`

Two connected subdomains with a shared boundary.

`geom.objects = { gobj_polygon([-2e-3 -8e-3;0 -8e-3;0 -6e-3;0 6e-3;0 8e-3;-2e-3 8e-3]), ... gobj_polygon([0 -6e-3;2e-3 -5e-3;2e-3 4e-3;0 6e-3]) }; hmax = 5e-4; hmaxb = hmax*ones(1,4); hmaxb(3) = hmax/5; grid = gridgen_gmsh( geom, 'hmax', hmax, 'hmaxb', hmaxb ); plotgrid( grid )`

Composite component with several subdomains.

`r1 = gobj_rectangle( 0, 0.11, 0, 0.12, 'R1' ); c1 = gobj_circle( [ 0.065 0 ], 0.015, 'C1' ); c2 = gobj_circle( [ 0.11 0.12 ], 0.035, 'C2' ); c3 = gobj_circle( [ 0 0.06 ], 0.025, 'C3' ); r2 = gobj_rectangle( 0.065, 0.16, 0.05, 0.07, 'R2' ); c4 = gobj_circle( [ 0.065 0.06 ], 0.01, 'C4' ); geom.objects = { r1 c1 c2 c3 r2 c4 }; geom = geom_apply_formula( geom, 'R1-C1-C2-C3' ); geom = geom_apply_formula( geom, 'R2+C4' ); grid = gridgen_gmsh( geom, 'hmax', [0.0025 0.05 0.0025] ); plotgrid( grid )`

Complex geometry with several holes and subdomains.

`w = 10e-4; L = 3*w; H = 5*w; p1 = gobj_polygon( [w/10 0;(L-w/4)/2 0;(L-w/4)/2 H;0 H;0 H/3], 'P1' ); p2 = gobj_polygon( [(L+w/4)/2 0;L 0;L H-H/3;L H;(L+w/4)/2 H], 'P2' ); r1 = gobj_rectangle( (L-w/4)/2, (L+w/4)/2, 0, H, 'R1' ); c1 = gobj_circle( [2*w/3 3*w], w/3, 'C1' ); c2 = gobj_circle( [2*w/3 2*w], w/3, 'C2' ); c3 = gobj_circle( [2*w/3 1*w], w/3, 'C3' ); c4 = gobj_circle( [L-w/2 4.5*w], w/8, 'C4' ); c5 = gobj_circle( [L-w 4.5*w], w/8, 'C5' ); c6 = gobj_circle( [L-w/2 4*w], w/8, 'C6' ); c7 = gobj_circle( [L-w 4*w], w/8, 'C7' ); c8 = gobj_circle( [L-w/2 3.5*w], w/8, 'C8' ); c9 = gobj_circle( [L-w 3.5*w], w/8, 'C9' ); c10 = gobj_circle( [L-w/2 3*w], w/8, 'C10' ); c11 = gobj_circle( [L-w 3*w], w/8, 'C11' ); geom.objects = { p1 p2 r1 c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 }; geom = geom_apply_formula( geom, 'P1-C1-C2-C3' ); geom = geom_apply_formula( geom, 'P2-C4-C5-C6-C7-C8-C9-C10-C11' ); hmaxb = zeros(1,21); hmaxb([5 20]) = w/50; grid = gridgen_gmsh( geom, 'hmax', w./[5 5 20], 'hmaxb', hmaxb ); plotgrid( grid )`

## Usage Notes

For geometries with multiple and overlapping geometry objects the
actual subdomain numbering will generally not correspond to the
geometry object numbering (two intersecting geometry objects will for
example create three or more subdomains and several internal
boundaries). In this case the actual subdomain and boundary numbering
for vector valued *hmax* and *hmaxb* arrays can easiest be visualized
and determined by first creating a coarse grid and switching to
*Equation/Subdomain* and *Boundary* modes, respectively.

*Gmsh* propagates the *hmax* and *hmaxb* values down to the specific
nodes in the mesh which means that it is currently not possible to
exactly define mesh sizes for subdomains and boundaries.

The temporary *Gmsh* generated *geo* and *msh* data files can be found
in the specified *fdir* directory (default given by the MATLAB *tempdir* function).

## References

[1] Gmsh home page - A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities.

[2] C. Geuzaine and J.-F. Remacle. Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering 79 (11), pp. 1309-1331, 2009.