We focus on a long-term 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, gradient-flow 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 block-based 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 SFB-funded researchers are allocated to such JWPs and not to the individual research groups.
In the above 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 analytically-oriented groups (left of the diagram) to the more numerically- and computationally-oriented (right), bringing to fruition the diversity of the SFB team expertises.