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Meshes

Table of Contents

Introduction

Feel++ provides some tools to manipulate meshes.
Here is a basic example that shows how to generate a mesh for a square geometry (source "doc/manual/tutorial/mymesh.cpp").

int main( int argc, char** argv )
{
// initialize Feel++ Environment
Environment env( _argc=argc, _argv=argv,
_desc=feel_options(),
_about=about( _name="mymesh" ,
_author="Feel++ Consortium",
_email="feelpp-devel@feelpp.org" ) );
// create a mesh with GMSH using Feel++ geometry tool
auto mesh = unitSquare();
// export results for post processing
auto e = exporter( _mesh=mesh );
e->addRegions();
e->save();
}
// main

As always, we initialize the Feel++ environment (see section FirstApp ).
The unitSquare() will generate a mesh for a square geometry. Feel++ provides several functions to automate the GMSH mesh generation for different topologies. These functions will create a geometry file .geo and a mesh file .msh. We can visualize them in GMSH. 

  gmsh <entity_name>.msh

Finally we use the exporter() (see Post-Processing and Visualization) function to export the mesh for post processing. It will create by default a Paraview format file .sos and an Ensight format file .case. 

  paraview <app_name>.sos

In this section, we present some of the mesh definition and manipulation tools provided by Feel++. For more information you can also see Gmsh.

Basic Meshes

There is a list of basic geometries you can automatically generate with Feel++ library.

Feel++ functionDimDescription</th
unitSegment();1Build a mesh of the unit segment \([0,1]\)
unitSquare();2Build a mesh of the unit square \([0,1]^2\) using triangles
unitCircle();2Build a mesh of the unit circle using triangles
unitHypercube();3Build a mesh of the unit hypercube \([0,1]^3\) using tetrahedrons
unitSphere();3Build a mesh of the unit sphere using tetrahedrons

Examples:
From "doc/manual/tutorial/myfunctionspace.cpp":

auto mesh = unitSquare();

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Load Meshes

loadMesh

You can use this function to:

  • load a .msh file and use the mesh data structure
  • load a .geo file and automatically generate a mesh data structure on this geometrical structure

Interface:

mesh_ptrtype loadMesh(_mesh, _filename, _refine, _update, physical_are_elementary_regions);

Required Parameters:

  • _mesh: a mesh data structure.

Optional Parameters:

  • _hsize (double): characteristic size of the mesh. This option will edit the .geo file and change the variable h if defined
    • Default: 0.1
    • Option: gmsh.hsize
  • _geo_variables_list (string): Set a list of variable that may be defined in a .geo file
    • Default: ""
    • Option: gmsh.geo-variables-list
  • _filename (string): filename with extension.
    • Default: "feel.geo"
    • Option: gmsh.filename
  • _depends (string): list of files (separated by , or ;) on which gmsh.filename depends
    • Default: ""
    • Option: gmsh.depends
  • _refine (boolean): optionally refine with refine levels the mesh.
    • Default: 0.
    • Option: gmsh.refine
  • _update (integer): update the mesh data structure (build internal faces and edges).
    • Default: true
  • _physical_are_elementary_regions (boolean): to load specific meshes formats.
    • Default: false.
    • Option: gmsh.physical_are_elementary_regions
  • _straighten (boolean): in case of curvilinear elements, straighten the elements which are not touching with a face the boundary of the domain
    • Default: true
    • Option: gmsh.straighten
  • _partitioner (integer): define the mesh partitioner to use:
    • Default: 1 (if Metis is available) 0 if not (CHACO)
    • Option: gmsh.partitioner


The file you want to load has to be in an appropriate repository.
Feel++ looks for .geo and .msh files in the following directories (in this order):

  • current path
  • paths that went through changeRepository(), it means that we look for example into the path from which the executable was run
  • localGeoRepository() which is usually "$HOME/feel/geo" (cf: Environment )
  • systemGeoRepository() which is usually "$FEELPP_DIR/share/feel/geo" (cf: Environment)

Examples:
Load a mesh data structure from the file "$HOME/feel/mymesh.msh".

auto mesh = loadMesh(_mesh=new mesh_type,
_filename="mymesh.msh");


Load a geometric structure from the file "./mygeo.geo" and automatically create a mesh data structure.

auto mesh = loadMesh(_mesh=new mesh_type,
_filename="mygeo.geo");


Create a mesh data structure from the file "./feel.geo".

auto mesh = loadMesh(_mesh=new Mesh<Simplex< 2 > > );

loadGMSHMesh

In order to load only .msh file, you can also use the loadGMSHMesh.

Interface:

mesh_ptrtype loadGMSHMesh(_mesh, _filename, _refine, _update, _physical_are_elementary_regions);

Required Parameters:

  • _mesh: a mesh data structure.
  • _filename: filename with extension.

Optional Parameters:

  • _refine: optionally refine with refine levels the mesh. Default =0.
  • _update: update the mesh data structure (build internal faces and edges). Default =true.
  • _physical_are_elementary_regions: to load specific meshes formats. Default = false.

The file you want to load has to be in an appropriate repository. See loadMesh.

Examples:
From "doc/manual/heatns.cpp":

mesh_ptrtype mesh = loadGMSHMesh( _mesh=new mesh_type,
_filename="piece.msh",
_update=MESH_CHECK|MESH_UPDATE_FACES|MESH_UPDATE_EDGES|MESH_RENUMBER );

From "applications/check/check.cpp":

mesh = loadGMSHMesh( _mesh=new mesh_type,
_filename=this->vm()["filename"].template as<std::string>(),
_rebuild_partitions=(Environment::worldComm().size() > 1),
_update=MESH_RENUMBER|MESH_UPDATE_EDGES|MESH_UPDATE_FACES|MESH_CHECK );

Create Meshes

createGMSHMesh

Interface:

mesh_ptrtype createGMSHMesh(_mesh, _desc, _h, _order, _parametricnodes, _refine, _update, _force_rebuild, _physical_are_elementary_regions);

Required Parameters:

  • _mesh: mesh data structure.
  • _desc: descprition. See further.

Optional Parameters:

  • _h: characteristic size. Default = 0.1.
  • _order: order. Default = 1.
  • _parametricnodes: Default = 0.
  • _refine: optionally refine with refine levels the mesh. Default =0.
  • _update: update the mesh data structure (build internal faces and edges). Default =true.
  • _force_rebuild: rebuild mesh if already exists. Default = false.
  • _physical_are_elementary_regions: to load specific meshes formats. Default = false.

To generate your mesh you need a description parameter. This one can be create by one the two following function.

geo

Use this function to create a description from a .geo file.

Interface :

gmsh_ptrtype geo(_filename, _h, _dim, _order, _files_path);

Required Parameters:

  • filename: file to load.

Optional Parameters:

  • _h: characteristic size of the mesh. Default = 0.1.
  • _dim: dimension. Default = 3.
  • _order: order. Default = 1.
  • _files_path: path to the file. Default = localGeoRepository().

The file you want to load has to be in an appropriate repository. See loadMesh.

Examples :
From "doc/manual/heat/ground.cpp":

mesh = createGMSHMesh( _mesh=new mesh_type,
_desc=geo( _filename="ground.geo",
_dim=2,
_order=1,
_h=meshSize ) );

From "doc/manual/fd/penalisation.cpp":

mesh = createGMSHMesh( _mesh=new mesh_type,
_desc=geo( _filename=File_Mesh,
_dim=Dim,
_h=Environment::vm(_name="hsize").template as<double>() ),
_update=MESH_CHECK|MESH_UPDATE_FACES|MESH_UPDATE_EDGES|MESH_RENUMBER );

domain

Use this function to generate a simple geometrical domain from parameters.

Interface :

gmsh_ptrtype domain(_name, _shape, _h, _dim, _order, _convex, \
_addmidpoint, _xmin, _xmax, _ymin, _ymax, _zmin, _zmax);

Required Parameters:

  • _name: name of the file that will ge generated without extension.
  • _shape: shape of the domain to be generated (simplex or hypercube).

Optional Parameters:

  • _h: characteristic size of the mesh. Default = 0.1.
  • _dim: dimension of the domain. Default = 2.
  • _order: order of the geometry. Default = 1.
  • _convex: type of convex used to mesh the domain. Default = simplex.
  • _addmidpoint: add middle point. Default = true.
  • _xmin: minimum x coordinate. Default = 0.
  • _xmax: maximum x coordinate. Default = 1.
  • _ymin: minimum y coordinate. Default = 0.
  • _ymax: maximum y coordinate. Default = 1.
  • _zmin: minimum z coordinate. Default = 0.
  • _zmax: maximum z coordinate. Default = 1.

Examples :
From "doc/manual/laplacian/laplacian.ccp":

mesh_ptrtype mesh = createGMSHMesh( _mesh=new mesh_type,
_desc=domain( _name=( boost::format( "%1%-%2%" ) % shape % Dim ).str() ,
_usenames=true,
_shape=shape,
_h=meshSize,
_xmin=-1,
_ymin=-1 ) );

From "doc/manual/stokes/stokes.cpp":

mesh = createGMSHMesh( _mesh=new mesh_type,
_desc=domain( _name=(boost::format("%1%-%2%-%3%")%"hypercube"%convex_type().dimension()%1).str() ,
_shape="hypercube",
_dim=convex_type().dimension(),
_h=meshSize ) );

From "doc/manual/solid/beam.cpp":

mesh_ptrtype mesh = createGMSHMesh( _mesh=new mesh_type,
_update=MESH_UPDATE_EDGES|MESH_UPDATE_FACES|MESH_CHECK,
_desc=domain( _name=( boost::format( "beam-%1%" ) % nDim ).str(),
_shape="hypercube",
_xmin=0., _xmax=0.351,
_ymin=0., _ymax=0.02,
_zmin=0., _zmax=0.02,
_h=meshSize ) );

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Todo

straightenMesh

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