Einladung zu einem Vortrag von:
Dr. Andrea Toselli
ETH Zürich
Dienstag, 13. Juli 2004
15:30 Uhr, HF 136
Domain decomposition preconditioners of Neumann-Neumann and FETI type for
hp approximations on highly anisotropic meshes
Solutions of elliptic boundary value problems
in polyhedral domains have corner and edge singularities.
Singularities may also arise at material interfaces.
In addition,
boundary layers often arise in flows with moderate or high Reynolds numbers
and in conductor materials with very large conductivity jumps,
at faces, edges, corners, and material interfaces.
Suitably graded anisotropic meshes, geometrically refined
toward corners, edges, faces, and/or interfaces,
allow to achieve an exponential rate
of convergence of hp finite element approximations.
In many practical applications, it is not merely a matter of speeding up
convergence, but of making computations possible, since simple h or p
approximations ion isotropic meshes
would require a prohibitively large number of unknowns.
The bottleneck for computations involving
such problems is often the solution of the corresponding
algebraic systems, which have huge condition numbers due to the
simultaneous effect of the large number of unknowns, the
large coefficient jumps,
the huge aspect ratios of the mesh, and small
parameters. Robust preconditioning is mandatory.
In the last years, we have been able to devise a
successful robust domain decomposition preconditioning strategy for
some hp approximations
of scalar problems on highly anisotropic two and three dimensional meshes.
More recently, this strategy has been extended to some edge element
approximations of electromagnetic problems.
Thanks to a particular choice of the subdomains and of the
coarse solvers, our preconditioners
ensure quasioptimality, scalability, robustness with respect to coefficient
jumps and huge aspect ratios of the meshes. We will illustrate these
features through numerical tests.
This page is part of a site using frames. Start your visit from the [main page: http://www.numa.uni-linz.ac.at]