Mesh definition¶

Geometric elements¶

The geometric components of a mesh can be subdivided by their dimension: vertices, edges, faces and hexes. A GeometricVertex is a 0D element which has a certain location in space. A GeometricEdge is a 1D element which is defined by 2 vertices. It has a length and direction, and therefore has a mapping function between a natural coordinate (defined as a value between -1 and 1) and the physical coordinate. The default shape is linear, but more general shapes can be implemented (by defining a corresponding mapping function). A GeometricFace is a 2D element, which is defined by 4 edges (in a circular order). The default shape is a flat plane, but a proper mapping function curved planes

A face also has a mapping function from the natural to physical domain, and this mapping is derived from the mappings of the 4 edges. Finally, the GeometricHex is a 3D element, which is defined by 6 faces.

Warning

Up to now 3D meshes (required for 3D (steady or with time stepping) or 2D space-time problems) have not been used frequently, and any use of 3D meshes will probably result in many runtime errors.

Geometric mesh¶

A general mesh consists of a collection of GeometricElements, and the construction of these geometric elements is handled by the GeometricMesh class. The contructor of the GeometricMesh assigns the mesh_data variable, which is obtained from the InternalMesh or the Gmsh_io class. The first of these is a Nemesis/MATLAB mesh definition , while the latter is obtained from a Gmsh input file ( with a msh extension). In both cases, the mesh_data variable will contain sufficient information for the GeometricMesh class to contruct the geometric elements (initGeometricElements function). Useful mesh object function are plot and plotLevels, which plot the active geometric elements and all geometric elements by their levels, respectively. More details on the meaning of active elements and element levels can be found in the explanation of adaptive mesh refinement.

Mesh elements¶

Mesh elements can be of type StaticElement or OctreeElement, and are the top dimension elements of the mesh. Their actual dimension depends on the underlying mesh dimension, therefore a mesh element can represent any dimension. The main difference between a StaticElement and an OctreeElement is that the latter can be refined.

Static / Octree mesh¶

Although an OctreeMesh object without refinement (maximum level is identically 0) is essentially a StaticMesh, constructing a mesh explicitly as a StaticMesh is different. The OctreeMesh class overloads certain functions from the StaticMesh class, which might in turn affect the efficiency of certain mesh operations. Note that simulation results should always be identical. If this is not the case there must be a bug in one of the implementations.