Until its early termination after seven months from the project start date, the
GEOLEARN project has brought its first objective to completion and successfully
developed new mixed-precision (MP) finite element methods (FEM). The
application of MP techniques to the FEM had never been investigated beforehand.
In particular, the GEOLEARN project has:
a) Derived the first rounding error analysis of FEM kernels and assembly. This
theory, submitted for publication, also accounts for MP implementations and MP
hardware accelerators, thus providing theoretical guidance for designing MP FEM
algorithms.
b) Designed new MP FEM implementation strategies and MP hardware-accelerated
algorithms which are provenly accurate as well as up to 60 times faster than
standard (double-precision) implementations. This work has been submitted for
publication and the resulting software is open source and freely accessible
online.
c) Identified new challenges and research opportunities in MP FEM algorithmic
design. Indeed, further research is still required to establish
production-ready MP FEMs with a mature enough technology to be incorporated
into open-source and commercial FEM software. Nevertheless, the project new
MP FEM algorithms are an important stepping stone towards this goal.
d) Created new inter-disciplinary and inter-university collaborations and
opened new avenues of investigation on MP methods.
e) Disseminated project results and ideas by organising minisymposia, giving talks
at conferences, and performing research visits.
The importance of this work lies in the fact that FEMs are ubiquitously used in
scientific computing and the widespread adoption of the new methods by the
scientific community can bring wide scientific impact.