Donnerstag, 10.01.2013, 14.00 Uhr
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 classiﬁed as either PDE-based or geometry based. We introduce yet
another new redistancing method for level set functions. This method applies
in a ﬁnite element setting and uses a gradient recovery technique. Based on the
recovered gradient a quasi-normal ﬁeld on the zero level of the ﬁnite element level
set function is deﬁned 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 ﬁnite 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 conﬁrm the theoretically predicted error behavior.
Zeit: 14:00 Uhr
Ort: Raum 149, Hauptgebäude, RWTH Aachen, Templergraben 55, 52056 Aachen