Project Area B: Discretization of pH systems

The pH-conforming modeling of dynamical systems is based on generalized concepts of en-
ergy, its preservation and dissipation. Furthermore, pH systems often arise as coupled multiphyscis
systems. These crucial structural features need to be complied with — but may also be lever-
aged — in simulations when the systems are discretized for numerical treatment and in the
numerical kernels that are used in actual computations. This poses new challenges for time
discretization of ODEs and DAEs, for space discretization, and, when computational demands
are high, for efficient numerical kernels. These are addressed in this project area.

Large scale simulations present challenges of their own. Multiphysics coupling, where differ-
ent software packages must be linked together, is considered in projects B01, B02 and B06.
Since structure-preserving time integration is necessarily implicit, linear and nonlinear systems
have to be solved, and in a large scale setting this must be done iteratively. B04 and B05
develop such iterative methods which specifically preserve or exploit structure-induced prop-
erties. These kernels tie in with the time discretization schemes considered in B01, B02, B03
and B06 where they are evaluated and where they ensure the computational efficiency of these
schemes.