Research activity


KIG: interactive geometry software.

Author: Dominique Devriese

2D automatic triangular mesh generator (TMG).

The TMG code is based on the advancing front technique, and provides a way to triangulate general domains in two dimension, possibly divided into subdomains, with holes, and with curved boundaries.

An example of typical domain divided into subdomains and a zoom of the resulting mesh after flipdiag and pigra regularization. The file protesi.tmg contains the domain description. The mesh in the picture is obtained from the domain description file with the TMG command sequence:
TMG> mesh
TMG> flipdiag
TMG> pigra
TMG> flipdiag

Here is another example...

Related information

  • Finite element mesh generation : a Web page maintained by Robert Schneiders at Lehrstuhl für angewandte Mathematik insbesondere Informatik.

    Motion by mean curvature.

    Click on the icon to view a detailed picture of a torus in the 4D space (a slice of it, actually) flowing by mean curvature. This picture is obtained with the POVRAY package. See also a few variants with different textures.

    Crystalline motion by mean curvature.

    We model motion by mean curvature in the particular case of a poligonal Wulff shape (crystalline anisotropy) by means of an Allen-Cahn type regularization, see [GoPa96A]. Simulations include the presence of an $x$ dependent forcing term.

    In this picture the solid line represents the Frank diagram of the anisotropy, and the dashed line represents the corresponding Wulff shape.

    This is the corresponding evolution starting from a circle (no forcing term).

    Here the anisotropy is nonconvex, and the convexified gives an hexagon. The "ears" in the Wulff shape correspond to the concave parts in the Frank diagram.

    Starting from a circle, our Allen-Cahn approach without convexification, gives the following result. Note the formation of wrinklings of the size of the spatial discretization.

    More simulations to be inserted here... see pictures here.

    Nonconvex motion by mean curvature, Perona-Malik equation.

    Text to be inserted here.....

    MP, Dec 6, 11