1,636 research outputs found
Schnelle Löser für partielle Differentialgleichungen
The workshop Schnelle Löser für partielle Differentialgleichungen, organised by Randolph E. Bank (La Jolla), Wolfgang Hackbusch(Leipzig), Gabriel Wittum (Heidelberg) was held May 22nd - May 28th, 2005. This meeting was well attended by 47 participants with broad geographic representation from 9 countries and 3 continents. This workshop was a nice blend of researchers with various backgrounds
Computing transition rates for the 1-D stochastic Ginzburg--Landau--Allen--Cahn equation for finite-amplitude noise with a rare event algorithm
In this paper we compute and analyse the transition rates and duration of
reactive trajectories of the stochastic 1-D Allen-Cahn equations for both the
Freidlin-Wentzell regime (weak noise or temperature limit) and finite-amplitude
white noise, as well as for small and large domain. We demonstrate that
extremely rare reactive trajectories corresponding to direct transitions
between two metastable states are efficiently computed using an algorithm
called adaptive multilevel splitting. This algorithm is dedicated to the
computation of rare events and is able to provide ensembles of reactive
trajectories in a very efficient way. In the small noise limit, our numerical
results are in agreement with large-deviation predictions such as
instanton-like solutions, mean first passages and escape probabilities. We show
that the duration of reactive trajectories follows a Gumbel distribution like
for one degree of freedom systems. Moreover, the mean duration growths
logarithmically with the inverse temperature. The prefactor given by the
potential curvature grows exponentially with size. The main novelty of our work
is that we also perform an analysis of reactive trajectories for large noises
and large domains. In this case, we show that the position of the reactive
front is essentially a random walk. This time, the mean duration grows linearly
with the inverse temperature and quadratically with the size. Using a
phenomenological description of the system, we are able to calculate the
transition rate, although the dynamics is described by neither
Freidlin--Wentzell or Eyring--Kramers type of results. Numerical results
confirm our analysis
Schnelle Löser für Partielle Differentialgleichungen
The workshop Schnelle Löser für partielle Differentialgleichungen, organised by Randolph E. Bank (La Jolla), Wolfgang Hackbusch (Leipzig), and Gabriel Wittum (Frankfurt am Main), was held May 22nd–May 28th, 2011. This meeting was well attended by 54 participants with broad geographic representation from 7 countries and 3 continents. This workshop was a nice blend of researchers with various backgrounds
A Vortex Method for Bi-phasic Fluids Interacting with Rigid Bodies
We present an accurate Lagrangian method based on vortex particles,
level-sets, and immersed boundary methods, for animating the interplay between
two fluids and rigid solids. We show that a vortex method is a good choice for
simulating bi-phase flow, such as liquid and gas, with a good level of realism.
Vortex particles are localized at the interfaces between the two fluids and
within the regions of high turbulence. We gain local precision and efficiency
from the stable advection permitted by the vorticity formulation. Moreover, our
numerical method straightforwardly solves the two-way coupling problem between
the fluids and animated rigid solids. This new approach is validated through
numerical comparisons with reference experiments from the computational fluid
community. We also show that the visually appealing results obtained in the CG
community can be reproduced with increased efficiency and an easier
implementation
Schnelle Löser für Partielle Differentialgleichungen
This workshop was well attended by 52 participants with broad geographic representation from 11 countries and 3 continents. It was a nice blend of researchers with various backgrounds
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