Implicit domain meshing

mmg3d allows to discretize and optimize an implicitly defined surface (i.e. a surface defined by a level-set function).

Since mmg2d and mmg3d have lot of options in common, it is possible to refer to the 2d examples for:

• isosurface discretization with mesh adaptation.

• input materials preservation (multi-material mode).

• bubble removal (small parasitic component deletion).

Standard level-set discretization

The starting point of this example is a mesh of a cube (cube.meshb) and the discrete level-set function defined at the mesh nodes elephant.sol displayed below.

Input isosurfaces

To split the domain on the 0 value of the level-set function, run the following command:

mmg3d_O3 cube -sol elephant.sol -ls -nr -hausd 0.001 -hgrad 1.3 -hmax 0.05

• Solution file name is specified using the -sol option.

• The -ls option states that the input .sol file is a level-set file and that mmg discretizes the implicit surface defined by the 0 isosurface of the level-set.

• A level-set function being a smooth function, ridges should not be detected and the -nr option is used.

• The cube mesh bounding box size being [1 x 1 x 1], a Hausdorff parameter (-hausd option) of 0.001 allows to have a good surface approximation.

• The authorized ratio between consecutive edges is increased using the -hgrad option.

• The -hmax option ensures that no edges longer than 0.05 will be created.

The output mesh consists in two domains separated by a surface that is an optimized mesh of the initial implicit surface, as illustrated below.

Note that mmg impose the reference of the isosurface and domains:

• The isosurface corresponds to reference 10.

• Interior volume has reference 3.

• Exterior volume outside has reference 2.

Output implicit surface mesh

Cross-section view through output mesh

Preservation of one specific subdomain and analysis mode

mmg allows to save a given subdomain of a mesh containing multiple subdomains using the -nsd option. For example, running mmg with the following command saves the domain of reference 3 (in this example, it corresponds to the elephant part of the output mesh):

mmg3d_O3 cube.o.meshb -noinsert -noswap -nomove -nsd 3

In this example, cube.o.meshb refers to the output mesh of the previous command line. The coupling of -noinsert, -noswap and -nomove options deactivates all remeshing operations, meaning that the mesh in cube.o.mesh is only analyzed and not modified. The output is displayed below.

Saving only subdomain of reference 3 using the -nsd option

Boundary level-set splitting

With the -lssurf option, it is possible to split domain boundaries along the level-set while leaving the interior of the mesh unsplit. In this example, input data consist in the peninsula.mesh meshfile and the peninsula.sol level-set file, represented below:

Initial data for surface level-set discretization

Level-set discretization of the surface only can be performed with the following command line:

mmgd3_O3 -lssurf peninsula.mesh

The result of this example is displayed below. With this option, mesh boundaries are split according to the input level-set function. Internal tetrahedra are not split. Note that all boundary references must be mapped in the reference file.

Boundaries split using -lssurf option