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Remeshing

We assess the mesh quality at fixed temporal intervals and use specific quality measures to decide whether to keep using the present mesh or remesh. For example, if the smallest angle of an element is less than a certain prescribed value, we remesh.

New mesh creation​

The default mode of remeshing is to create a new mesh preserving the old mesh's boundaries. The meshing libraries linked during the build are resued: triangle for 2D and tetgen for 3D. To assist the meshing process, DES provides a point set for the meshing libraries to start with. However, a group of nodes in the deformed mesh may be removed from the point set if any of the following criteria is met:

  • Left outside of the new boundaries when a deformed or displaced boundary is restored to the initial configuration
  • Surrounded only by small elements

Once all criteria are enforced, a final list of nodes is collected and used for constructing a new mesh. During the process, new nodes might be inserted into the mesh or the mesh topology changed through edge-flipping (see the figure below) during the triangulation.

edge flipping during remeshing (above) Plastic strain distribution on a mesh before and after remeshing. Solid and dashed white lines are new and old element edges. Pink circles are newly added nodes.

Mesh optimization​

As described in https://geoflac.github.io/des3d/docs/tutorial/usingmmg, a user can choose link MMG when building DES. MMG performs mesh optimization allowing a metric-based element size variation and the metric itself can be defined in terms of one of the physical variables like accumulated plastic strain.

Variable mapping from old to new mesh​

After the new mesh is created, the boundary conditions, derivatives of shape function, and mass matrix have to be re-calculated.

Also, an inter-mesh mapping of variables is performed. For data associated to nodes (e.g., velocity and temperature), we use linear interpolation of the data from the old mesh to evaluate the field at the new nodal location. For data associated to elements (e.g., strain and stress), we use a nearest-neighbor mapping.