The concept
We focus on a longterm program of collaborative efforts
aimed at
reducing the complexity of such systems by revealing, exploiting, and preserving
mathematical structures.
The term structure is used here to indicate some relevant background framing
of the PDE system such as conservation or dissipation of physical
quantities, gradientflow evolution, asymptotic behavior, qualitative properties
of trajectories, emergence of scale effects.
The tenet of this SFB is that
taking full advantage of
such structures plays a pivotal role for the successful treatment of complex
PDE systems. This theme cuts across modeling, analysis,
numerical analysis, and implementation and necessitates collaboration
across traditional field boundaries. For example, in one direction qualitative properties of solutions, conservation of
physical quantities, correct asymptotic behavior at the continuum
level must be effectively reproduced by approximations in order to
achieve improved performances. In the other direction,
the need of blockbased simulations calls for the development of
efficient solvers, which in turn are strongly affected by problem
formulations and ultimately by modeling choices.
Such an extensive, intradisciplinary scientific effort is only possible
with the appropriate organizational structure. The SFB features
a totally integrated
scientific program based on a network of complementary
expertises. This is realized by Joint Work Packages
(JWPs) connecting two or more research groups. All the SFBfunded researchers are allocated to such JWPs
and not to the individual research groups:
In the diagram each edge represents a JWP.
The JWP network interlaces the whole SFB and bridges over the whole
span of competencies required by the project (from modeling to analysis and
stochastics, to numerics and software development). In particular, it
strictly connects the more analyticallyoriented groups (left of the diagram) to the more numerically and
computationallyoriented (right), bringing to fruition the diversity of
the SFB team expertises.
