分野別セミナー

講演1 [第263回 15:00-15:35]
題目: Comparison of the Lagrangean and level-set method
　 　　　 for the Willmore flow
講演者: Tomas Oberhuber (チェコ工科大学)


講演2 [第264回 15:40-16:15
題目: Numerical issues behind the MR-DTI visualization algorithm
講演者：Pavel Strachota (チェコ工科大学)


講演3 [第265回 16:20-16:55]
題目: FEM for flow and pollution transport in 2D urban canopy
講演者：Petr Bauer (チェコ工科大学)

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講演1要旨:
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.


講演2要旨:
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.


講演3要旨:
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.


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