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Comparison of the Lagrangean and level-set method for the Willmore flow etc.

Hold Date
2010-11-18 15:00〜2010-11-18 17:00
Seminar Room 3, Faculty of Mathematics building, Ito Campus
Object person
Tomas Oberhuber (Czech Technical University) and two others


Lecture1(the 59th lecture, 15:00-15:35)
Title:Comparison of the Lagrangean and level-set method
for the Willmore flow
Speaker:Prof. Tomas Oberhuber (Czech Technical University)
We present two numerical methods for the Willmore flow of the
planar curves. The Lagrangean approach works with parametrised
curves. Discretisation leads to a "string" of nodes approximating
the curve. To be able to compute evolution of such curve,
redistribution of the nodes along the curve is necessary. There
are several methods of the redistribution aim of which is to keep
equidistant distribution of the nodes. The main advantage of this
method is its efficiency, on the other hand it does not allow any
changes in topology of the curve (merging or splitting). In this
case the level-set method is good choice. It expresses the curve
implicitly which increases the dimension of the problem by one.
Unfortunately, it also means more expansive computations.
We present numerical schemes for both methods together with
comparison on several non-trivial examples and we also demonstrate
experiments with topological changes obtained by the level-set

Lecture2(the 60th lecture, 15:40-16:15)
title:Numerical issues behind the MR-DTI visualization algorithm
Speaker:Prof. Pavel Strachota 氏(Czech Technical University)
For the purpose of MR-DTI data visualization, we have developed
a numerical algorithm based on a mathematical model of texture
diffusion. Accompanied by data preprocessing and postprocessing
procedures, this algorithm forms the cornerstone of the MEGIDDO
(Medical Employment of Generating Images by Degenerate Diffusion
Operator) software tool, which is briefly introduced in this
contribution. Afterwards, we focus on investigating the
properties of the numerical solution methods. Emphasis is put
on the assessment of several numerical schemes with respect to
artificial diffusion. Both visual and quantitative methods
for scheme comparison are discussed.

Lecture3(the 61th lecture, 16:20-16:55)
title:FEM for flow and pollution transport in 2D urban canopy
Speaker:Prof. Petr Bauer(Czech Technical University)
We develop a mathematical model of air flow and pollution
transport in 2D urban canopy. The model is based on the
Navier-Stokes equations for viscous incompressible flow and
on the advection-diffusion equation describing pollution
transport. The solution is obtained by means of finite element
method. We use the non-conforming Cruzeix Raviart elements
for velocity and pressure, and linear Lagrange elements for
concentration. The resulting linear systems are solved by
multigrid methods. We present computational studies of air
flow and pollutant dispersion.

*This seminar is held with Phenomena Mathematics Seminar.