Mesh Size Specification

Three levels of mesh size specification are considered

• the global mesh size specification,
• the local mesh size specification, and
• the adaptive mesh size specification.

The global mesh size specification uses global weight functions to control the mesh size description over the domain. The local mesh size specification concept prescribes the desired mesh size variation on model entities. In the adaptive mesh size specification strategy, various mesh size sources, built according to the preceding problem analysis, are used.

Currently only the local and adaptive mesh size specifications are implemented. The local mesh size specification consists of two parts

• the required mesh size specification and
• the curvature-based mesh size control.

The former concept is used to explicitly prescribe the mesh size at individual model entities. Mesh size specification is stored at each vertex and at each control point of any curve or surface. These values are used to extract the mesh size specification on a curve or surface. Moreover, each model entity (except vertices) stores an upper bound limit on mesh size which is not allowed to be exceeded.

Similar expressions to the ones describing the geometry of rational Bezier curves and surfaces are used to interpolate the local mesh size specification at control points over the curve and surface. The mesh size extracted from a curve mesh size specification has the form

where is the required mesh size at point on the curve, are the mesh size specifications at Bezier control points, and the other symbols have the same meaning as in Eq. (1). A similar formula can be written for the extraction of the required mesh size on a surface

where is the required mesh size at point on the surface, are the mesh size specifications at Bezier control points. The remaining variables have the the same meaning as in Eq. (2).

The latter concept is employed to enable an accurate representation of a curve or surface by its discretization even if no particular mesh size is required. The criterion is based on the ratio (curvature rate) between the appropriate mesh size and the radius of curvature at a given location on the curve or surface. The default ratio is equal to 1, which corresponds to the discretization of a circle to 6 segments of the same length equal to the radius of the circle. The curvature-based mesh size control is performed implicitly. Its suppression may resolve in an unrecoverable error during mesh generation.

The adaptive mesh size specification is based on a background mesh with the mesh size specification at nodes and linear interpolation over the elements (edges, triangles, and tetrahedrons).