Münchner Mathematische KalenderKalender mit mathematischen Vorträgen im Raum München2018-03-12T07:59:56Ztag:mathcal.ma.tum.de,2013-04-10:/feed/filter2/year2018/month307.03.2018 16:00 Martin Siebenborn (Universität Hamburg): Shape optimization algorithms for interface identification2018-02-27T21:09:19ZMartin Siebenborn (Universität Hamburg)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20180116180000In many applications, which are modeled by partial differential equations (PDEs), there is a small
number of materials or parameters distinguished by interfaces to be identified. While classical approaches
in the field of optimal control yield continuous solutions, a spatially distributed, binary variable is closer
to the desired application. It is thus favorable, to treat the shape of the interface between an active and
inactive control as the variable. Moreover, since the involved materials may form complex contours, high
resolutions are required in the underlying finite element method.
We investigate a combination of classical PDE constrained optimization methods and a rounding
strategy based on shape optimization for the identification of interfaces. The goal is to identify the
location of pollution sources in fluid flows represented by a control that is either active or inactive.
While the most intuitive approach would be to treat this as a combinatorial problem and to decide cell
by cell whether it is polluted or not, computational complexity and mesh-dependent solutions are major
drawbacks. These issues can be circumvented by the algorithm we present here. Moreover, it is shown
how the topology of an inaccurate initial guess for the pollutant locations can be corrected during the
shape optimization, which is a typical problem in that field.
References
[1] M. Siebenborn. A shape optimization algorithm for interface identification allowing topological
changes. arxiv.org/abs/1711.02535, 2018.
[2] M. Siebenborn and K. Welker. Algorithmic aspects of multigrid methods for optimization in shape
spaces. SIAM Journal on Scientific Computing, 39(6):B1156–B1177, 2017.
12.03.2018 15:00 Dr. Sebastian Riedel (Technische Universität Berlin): Rough differential equations with unbounded drift2018-03-02T08:00:47ZDr. Sebastian Riedel (Technische Universität Berlin)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20180302085832We consider rough differential equations with a possibly unbounded drift term. It turns out that the usual one-sided growth conditions are not sufficient to guarantee non-explosion of the solution in finite time. We then provide a further condition under which non-explosion can be assured. Some applications in stochastic analysis are discussed.
Joint work with M. Scheutzow (Berlin).
14.03.2018 16:30 Prof. Dr. Vincent Tassion (ETH Zürich): The phase transition for Boolean percolation2018-03-12T07:59:56ZProf. Dr. Vincent Tassion (ETH Zürich)tag:mathcal.ma.tum.de,2013-04-10:/talk/created/20171130101331Based on joint works with Daniel Albergh, Hugo Duminil-Copin, Aran
Raoufi and Augusto Teixeira.
Consider Poisson-Boolean percolation in R^d. Around every point of a
Poisson point process of intensity lambda, draw independently a ball
with random radii.
I will discuss the sharpness of the phase transition in lambda for this
process. In particular, I will present sharp bounds for the cluster of
the origin to have radius greater than n in the subcritical regime, and
how these bounds depend on the radii distributions.
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