Thursday, 10.01.2013 02:00 pm

A finite element level set redistancing method based on gradient recovery

Prof. Arnold Reusken (IGPM, RWTH Aachen)


In level set methods one often uses a so-called reinitialization or redistancing
(or reparametrization) procedure. Since the introduction of the reinitialization
approach many of such methods have been proposed in the literature. Most of
these can be classi?ed as either PDE-based or geometry based. We introduce yet
another new redistancing method for level set functions.  This method applies
in a ?nite element setting and uses a gradient recovery technique. Based on the
recovered gradient a quasi-normal ?eld on the zero level of the ?nite element level
set function is de?ned and from this an approximate signed distance function
is determined. For this redistancing method rigorous error bounds are derived.
For example, the distance between the original zero level and the zero level after
redistancing can be shown to be bounded by chk+1 , if ?nite elements of degree
k are used in the discretization. Comparable error bounds are not available for
other redistancing methods known in the literature.  In the talk some popular
reinitialization  methods  will  be  reviewed  and  the  new  method  is  explained.
Results of numerical experiments with the gradient recovery based redistancing
method are presented that con?rm the theoretically predicted error behavior.

Time: 02:00 pm

Location: Room 149, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen