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## Seminars

### 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
- Place
- Seminar Room 3, Faculty of Mathematics building, Ito Campus
- Object person
- Speaker
- Tomas Oberhuber (Czech Technical University) and two others

Program

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）

Summary：

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

method.

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）

Summary：

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）

Summary：

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.