Full GUI and CLI Gmsh Mesh Generator Integration with FEATool

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FEATool-Gmsh Mesh Generator Integration

This FEATool update patch fully integrates the Gmsh finite element mesh and grid generator with FEATool [1][2]. Both Matlab and Octave command line interface (CLI) usage is supported with the new gridgen_gmsh function, as well as the FEATool GUI with a new dedicated Gmsh button 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.

Gmsh CAD Step File Import And Mesh Generation Tutorial - 3D

The new gridgen_gmsh function attempts to convert FEATool geometries to Gmsh geo data file format, call Gmsh in non-interactive mode to generate a corresponding finite element FEM mesh, and parse and import 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, please ensure that the latest version of FEATool is installed (version 1.7) with either Matlab or Octave, and download the Gmsh update and integration patch from the link below

FEATool-Gmsh Integration and Update Patch

Extract the contents of the featool-gmsh-patch.zip archive into the FEATool installation directory, or alternatively manually copy the two files listed below

gridgen_gmsh.m  >  featool/gridgen_gmsh.m
grid_mode.m     >  featool/gui/grid_mode.m

If the Gmsh mesh generator binary is not present or cannot be found in the featool/lib/gmsh folder, then the gridgen_gmsh function will attempt to automatically download, and install it by itself.

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

GUI Usage

Once installed, the updated GUI will in 2D and 3D grid mode show a new button labeled Gmsh. Pressing this opens the Gmsh Grid Generation dialog box with two edit fields for entering hmax, and hmaxb.

Matlab Grid and Mesh Generation with Gmsh and the FEATool GUI
  • 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 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 and Octave command lines 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
hmaxp       scal/arr {[]}              Target grid size for vertices/grid points
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  {false}           Delete (clean) Gmsh help files
instdir     string   {'featool/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). hmaxp prescribes mesh sizes directly on points. HMAXP values takes precedence over HMAXB values, which in turn take precedence over HMAX values.

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 or Octave command line interface.


Grid Generation Examples

Matlab Mesh Generation Gmsh Grid Examples
  1. Unit square with uniform global grid size set to 0.1.

    grid = gridgen_gmsh( {gobj_rectangle()}, 'hmax', 0.1 );
    plotgrid( grid )
    
  2. Unit square with finer grid on top boundary.

    grid = gridgen_gmsh( {gobj_rectangle()}, 'hmax', 0.5, ...
                         'hmaxb', [0.5 0.05 0.05 0.05] );
    plotgrid( grid )
    
  3. 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 )
    
  4. Two connected subdomains with a shared boundary.

    geom.objects = { gobj_rectangle(-2e-3,0,-8e-3,8e-3), ...
                     gobj_polygon([0 -6e-3;2e-3 -5e-3;2e-3 4e-3;0 6e-3]) };
    hmax  = 5e-4;
    grid  = gridgen_gmsh( geom, 'hmax', hmax );
    plotgrid( grid )
    
  5. 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' );
    
    hmax  = 0.005;
    grid  = gridgen_gmsh( geom, 'hmax', hmax );
    plotgrid( grid )
    
  6. 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' );
    
    hmax = w/5;
    grid = gridgen_gmsh( geom, 'hmax', hmax );
    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.

If the Triangle mesh generator patch has been installed, the Gmsh GUI update will remove the toolbar buttons to call the Triangle grid generator (however, gridgen_triangle may still be called from the command line ).

The temporary Gmsh generated geo and msh data files can be found in the specified fdir directory (default given by the Matlab and Octave 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.

Category: grid

Tags: external gmsh

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