The open source, C++ deal.II Finite Element library (dealii.org) uses Kokkos for performance portability for the efficient numerical solution of partial differential equations on GPUs.
We will provide an overview of the deal.II library and how large-scale finite element problems are solved in parallel using a matrix-free, adaptive, parallel geometric multigrid method. Then we describe the current status of the adoption of Kokkos and the challenges of having the PDE defined in user codes.
We close with numerical experiments of matrix-free and matrix-based methods on CPUs and GPUs.

We present a solver for incompressible, high-Reynolds-number flow around a rotating fan, built on NGSolve and aimed at the design of heat-pump units. The flow is discretised with a mass-conserving mixed stress (MCS) method in H(div), giving pointwise divergence-free velocities, and advanced in time by an incremental pressure-correction (IPCS) splitting: an implicit MCS viscous step, a matrix-free upwind-DG convection step run on the GPU, and a hybridised mixed-Poisson pressure projection. Rotor and stator are meshed independently and coupled across a non-matching sliding interface using mortar methods, rebuilt each step for the velocity, pressure-trace and upwind-flux couplings.
We validate the method on a fan in a wall mount and then apply it to a full heat-pump unit, with a detailed fan and a homogenised heat exchanger. We close with an outlook on reinforcement-learning-driven design of a robust, parametrised flow rectifier.
*Joint work with the FFG-funded consortium (SCCH Hagenberg, TU Wien, Windpuls, EBM-papst, IDM Wärmepumpen).

.