FEniCS was started in 2003 as an umbrella for open-source software components with the goal of automated solution of Partial Differential Equations based on the mathematical structure of the Finite Element Method (FEM).

FEniCS-HPC is the collection of FEniCS components around DOLFIN-HPC, a branch of DOLFIN with the focus of strong parallel scalability and portability on supercomputers, and Unicorn, the Unified Continuum solver for continuum modeling based on the Direct FEM Simulation (DFS) methodology described below, with breakthrough applications in parameter-free adaptive prediction of turbulent flow and fluid-structure interaction.

The FEniCS-HPC components are developed in our BitBucket Git repositories.

##### Direct FEM Simulation (DFS)

Our DFS methodology is based on a piecewise linear approximation in space and time and with a numerical stabilization in the form of a weighted least squares method based on the residual. The methodology has several unique aspects which we hope can advance the field in new directions:

- The incompressible Navier-Stokes Equations (NSE) are discretized directly, without applying any filter. Thus, the method does not approximate any Large Eddy Simulation (LES) filtered solution, but is instead an approximation of a weak solution, satisfying the weak form of the NSE.
- For this method, we have a posteriori error estimates of quantities of interest with respect to a weak solution, which form the basis for our adaptive mesh refinement algorithm. The a posteriori error estimates are based on the solution of an associated adjoint problem with a goal quantity (such as a drag coefficient) as data.
- We model turbulent boundary layers by a slip boundary condition which is a good approximation for small skin friction stress, which gives enormous savings in computational cost by not having to resolve a very thin boundary layer.

##### References

Johan Hoffman, Johan Jansson, Niclas Jansson, FEniCS-HPC: Automated predictive high-performance finite element computing with applications in aerodynamics, Lecture Notes in Computer Science, 2016

Johan Hoffman, Johan Jansson, Niclas Jansson, Rodrigo Vilela de Abreu, Claes Johnson, Computability and Adaptivity in CFD, Encyclopedia of Computational Mechanics, 2016

Johan Hoffman, Johan Jansson, Rodrigo Vilela de Abreu, Niyazi Cem Degirmenci, Niclas Jansson, Kaspar Müller, Murtazo Nazarov, Jeannette Hiromi Spühler, Unicorn: Parallel adaptive finite element simulation of turbulent flow and fluid-structure interaction for deforming domains and complex geometry, Computers & Fluids, 2013

Johan Hoffman, Johan Jansson, Niyazi Cem Degirmenci, Niclas Jansson, Murtazo Nazarov, Unicorn: a unified continuum mechanics solver; in automated solution pf differential equations by the finite element method, Lecture Notes in Computational Science and Engineering, 2011