4.2.1 Characteristic lengths

There are two ways to specify the size of the mesh elements for a given geometry:

1. You can specify characteristic lengths at the points of the geometrical model (with the Point command: see Points). The size of the mesh elements will then be computed by linearly interpolating these characteristic lengths on the initial mesh (see Mesh: finite element mesh generation). This might sometimes lead to over-refinement in some areas, so that you may have to add “dummy” geometrical entities in the model in order to get the desired element sizes.

   This method works with all the algorithms implemented in the mesh module. The final element sizes are of course constrained by the structured algorithms for which the element sizes are explicitly specified (e.g., transfinite and extruded grids: see Structured grids).

2. You can specify characteristic lengths using mesh size “fields”. Various fields exist:
   • A PostView field specifies an explicit background mesh in the form of a scalar post-processing view (see Post-processing commands, and File formats) in which the nodal values are the target element sizes. This method is very general but it requires a first (usually rough) mesh and a way to compute the target sizes on this mesh (usually through an error estimation procedure, in an iterative process of mesh adaptation).

     (Note that you can also load a background mesh directly from the command line using the -bgm option (see section Command-line options), or in the GUI by selecting `Apply as background mesh' in the post-processing view option menu.)

   • A Box field specifies the size of the elements inside and outside of a parallelipipedic region.
   • A Threshold field specifies the size of the mesh according to the distance to some geometrical entities. These entities can for example be geometry points and lines specified by an Attractor field.
   • A MathEval field specifies the size of the mesh using an explicit mathematical function.
   • A Min field specifies the size as the minimum of the sizes computed using other fields
   • …

   All target element sizes specified by fields can also be constrained by the characteristic lengths defined in the geometrical model if the Mesh.ConstrainedBackgroundMesh option is set.

   Fields are supported by all the algorithms except those based on Netgen.

Here are the mesh commands that are related to the specification of characteristic lengths:

Characteristic Length { expression-list } = expression;

Modifies the characteristic length of the points whose identification numbers are listed in expression-list. The new value is given by expression.

Field[expression] = string;

Field[expression].string = char-expression | expression | expression-list;

Background Field = expression;