1.2 Mesh: finite element mesh generation

A finite element mesh is a tessellation of a given subset of the three-dimensional space by elementary geometrical elements of various shapes (in Gmsh's case: lines, triangles, quadrangles, tetrahedra, prisms, hexahedra and pyramids), arranged in such a way that if two of them intersect, they do so along a face, an edge or a node, and never otherwise. All the finite element meshes produced by Gmsh are considered as “unstructured”, even if they were generated in a “structured” way (e.g., by extrusion). This implies that the elementary geometrical elements are defined only by an ordered list of their nodes but that no predefined order relation is assumed between any two elements.

The mesh generation is performed in the same bottom-up flow as the geometry creation: lines are discretized first; the mesh of the lines is then used to mesh the surfaces; then the mesh of the surfaces is used to mesh the volumes. In this process, the mesh of an entity is only constrained by the mesh of its boundary(1). This automatically assures the conformity of the mesh when, for example, two surfaces share a common line. But this also implies that the discretization of an “isolated” (n-1)-th dimensional entity inside an n-th dimensional entity does not constrain the n-th dimensional mesh. Every meshing step is constrained by the characteristic length field, which can be uniform, specified by characteristic lengths associated with points in the geometry, or defined by general “fields” (a scalar field defined on another mesh using post-processing view, threshold fields associated with point or line “attractors”, etc.).

For each meshing step, all structured mesh directives are executed first, and serve as additional constraints for the unstructured parts (2).