
Schedule
By hovering the cursor over a title, you can see the abstract of the corresponding presentation.
Thursday, January 22, 2009
08:4509:15 
Welcome  

09:1509:30 
Introduction  
M. Postel 
09:3010:15 
Fully adaptive multiresolution methods for evolutionary PDEs
We present efficient fully adaptive numerical schemes for evolutionary
partial differential equations based on a finite volume (FV)
discretization with explicit time discretization. A multiresolution
strategy allows local grid refinement while controlling the approximation
error in space. The costly fluxes are evaluated on the adaptive grid only.
For time discretization we use an explicit RungeKutta scheme of
secondorder with a scaledependent time step. On the finest scale the
size of the time step is imposed by the stability condition of the
explicit scheme. On larger scales, the time step can be increased without
violating the stability requirement of the explicit scheme. Embedded
RungeKutta methods of second and third order are then used to choose
automatically the new time step while controlling the approximation error
in time. Nonadmissible choices of the time step are avoided by limiting
its variation.
The implementation of the multiresolution representation uses a dynamic
tree data structure, which allows memory compression and CPU time
reduction. This new numerical scheme is validated using different
classical test problems in one, two and three space dimensions. The gain
in memory and CPU time with respect to the finite volume scheme on a
regular grid is reported, which demonstrates the efficiency of the new
method. 
(PDF) 
K. Schneider 
10:1511:00 
Multiresolution acceleration methods in three dimensions
We show a version of Harten's cellaveraged multiresolution (MR)
scheme that works on threedimensional unstructured meshes. The MR
method uses the difference in information between adjacent grid levels
on a set of nested grids for determining active and inactive grid
cells. This boils down to computing the wavelet decomposition known to
be a rich source of regularity information. Shocks, contact
discontinuities, reaction fronts, or any other inviscid and viscous
flow features can be identified and tracked in a timeaccurate
fashion. In active regions the underlying finite volume scheme is
solved in the usual manner, whereas in smooth regions an inexpensive
interpolation of the numerical divergence replaces both flux
computations and reconstruction. Thus the simulation becomes
significantly more efficient without any loss of accuracy compared to
the finest grid available. The combined finite volumeMR method will
be described followed by 2 and 3D examples on unstructured meshes.
 
B. L. Bihari 
11:0011:30 
Coffee break 

11:3012:00 
Parallelization of multiscalebased grid adaptation using space filling curves 
(PDF) 
S. Mogosan 
12:0012:30 
Utilisation of Harten multiresolution in
scientific computing: two examples 
(PDF) 
G. Chiavassa 



12:3014:00 
Lunch 




14:0014:45 
Combining multiresolution and anisotropy:
theory, algorithms and open problems
Multiresolution adaptive method are known to be of efficient use
in the numerical solution of PDE's, providing with efficient compression
and data structure. In these methods the local refinement of elements/volumes
is usually isotropic.
In this talk, we shall address the issue of deriving multiresolution
adaptive methods based on anisotropic triangulations. We discuss
the approximation theory available for such triangulations. When the
function to be approximated is known to us, we propose a greedy
algorithm which has the ability to generate adaptive hierarchical
triangulations that exhibit a locally optimal aspect ratio, resulting
in an optimal convergence rate. We finally discuss the difficulties
which are to be dealt with when applying these ideas to PDE's. 
(PDF) 
A. Cohen 
14:4515:15 
Guaranteed and robust discontinuous Galerkin
a posteriori error estimates for convectiondiffusionreaction problems
We propose and study a posteriori error estimates for
convectiondiffusionreaction problems approximated by weighted
interiorpenalty discontinuous Galerkin methods. Our estimates are fully
robust in the singularly perturbed regimes for the error measured in a norm
consisting of the energy (semi)norm, a dual norm of the skewsymmetric part
of the differential operator, and a suitable contribution of the
interelement jumps of the discrete solution. This means that the effectivity
index (overestimation factor) is independent of the size of the convection
or reaction terms. The estimates do not involve any undetermined constants,
are fully computable, and can thus be used to the actual error control. We
achieve this feature by introducing H(div)conforming diffusive and
convective flux reconstructions. Finally, our estimates are locally
efficient, whence they are also suitable for adaptive mesh refinement.
Numerical experiments illustrate these theoretical results. 
(PDF) 
M. Vohralik 
15:1515:45 
Coffee break 

15:4516:15 
Simulation of incompressible flows with artificial
compressibility using fully adaptive multiscale schemes 

Y. Stiriba 
16:1516:45 
A new strategy for adapting timestep in the Local Time Stepping method
applied to hyperbolic PDEs
We are concerned with the numerical simulations of twophase flows representing oil transportation along a 1D pipeline, over a long timerange. Such problems are modeled by a highly nonlinear system of partial differential equations of conservations laws. For this kind of evolutionary problems, we make use of the LagrangeProjection finitevolume scheme coupled with the Multiresolution and the Local Time Stepping methods. Indeed, employing these two adaptive methods allows us to speed up the computation while maintaining the accuracy of the results.
In this talk, we want to emphasize on the new strategy for computing the timestep in the context of the Local Time Stepping method applied to hyperbolic PDEs system. More specifically, instead of using constant "micro" timesteps, we propose to recalculate them after each local evolution of the solution on the adaptive grid. These varying adequate timesteps must decrease during each "macro" timestep in order to satisfy the stability of the numerical scheme. Numerical results as well as CPU time of realistic simulations will be presented to show the efficiency of such a strategy. 
(PDF) 
Q. L. Nguyen 
Friday, January 23, 2009
09:3010:15 
Adaptive methods for the Vlasov equation
In this talk we shall give a review of the work we have
performed on the development of adaptive solvers for the Vlasov
Poisson and VlasovMaxwell equations. Different multiresolution
techniques have been compared, in particular interpolating wavelets
and hierarchical finite elements. We shall address the refinement
strategies and also the data structures and efficient parallel
implementation techniques which remain one of the bottlenecks of such
solvers in higher dimensions. Our solutions in four dimensional phase
space shall be detailed. 
(PDF) 
E. Sonnendrücker 
10:1511:00 
Waveletbased CVS method to solve a convectiondominated problem:
the numerical simulation of turbulence 
(PDF) 
M. Farge 
11:0011:30 
Coffee break 

11:3012:00 
How to predict accurate grids in adaptive semiLagrangian schemes
In this talk I will present a new class of adaptive semiLagrangian schemes
 based on performing a semiLagrangian method on adaptive interpolation
grids  in the context of solving nonlinear transport problems with
underlying smooth characteristic flow.
I will describe two frameworks for implementing adaptive interpolations,
namely multilevel finite elements and interpolatory wavelets. For both
discretizations, I introduce a notion of good adaptivity to a given function, and show
that it is preserved by a lowcost prediction algorithm which transports multilevel
grids along any smooth numerical flow. Error estimates are then established for the
resulting ``predict and readapt'' schemes. As for the wavelet case, these results are new and also apply
to highorder interpolation.

(PDF) 
M. CamposPinto 
12:0012:30 
Local time steps for a finite volume scheme
We present a strategy for solving timedependent problems on grids with local refinements in time using different time steps in different regions of space. We discuss and analyze two conservative approximations for a parabolic equation, based on finite volume with piecewise constant projections and domain decomposition techniques. Next we present an iterative method for solving the compositegrid system that reduces to solution of standard problems with standard time stepping on the coarse and fine grids. At every step of the algorithm, conservativity is ensured. Finally, numerical results illustrate the accuracy of the proposed methods. 
(PDF) 
I. Faille 



12:3014:00 
Lunch 




14:0014:45 
Using Harten’s multiresolution Framework
on existing codes for hyperbolic PDEs 
(PDF) 
R. Donat 
14:4515:00 
Closing remarks 
S. Müller 


