Many multi-physics problems allow for a complexity reduction. In
this talk, we present surface and volume based coupling schemes
which give rise to one or bi-directionally coupled algebraic
systems. In most cases, no analytical solution can be found and one
has to exploit fast and reliable numerical schemes to obtain
accurate approximations. The discretization has to be stable and
flexible to result in efficient numerical solvers. Firstly, we
discuss dimensional reduced models for flow problems, e.g.,
subproblems of co-dimension one or two. Secondly, we illustrate how
simple and lean low order methods go hand in hand with highly
scalable parallel solvers. Here special focus is on locally
conservative methods, e.g., for energy, surface traction or mass. To
get a better understanding, we illustrate spurious numerical
oscillation for non-conservative methods. Although optimal a priori
order estimates are attractive from the computational point of view,
they do not necessarily give rise to short run-times on modern
architectures. Here we show how domain partitioning strategies can
be used to obtain excellent performance. Part of this work is
supported by the DFG priority programme "Software for exascale
computing".
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