NektarIR at the 50th FEM@LLNL seminar

10 February 2026 event

David Moxey and Edward Erasmie-Jones gave the 50th talk in the FEM@LLNL seminar series, run by the MFEM team at Lawrence Livermore National Laboratory. The talk was on NektarIR: a domain-specific compiler for high-order finite element operations on heterogeneous hardware, and the recording is on YouTube.

The problem it addresses is that high-performance computing hardware has become heterogeneous and GPU-dominated, so the kernels that evaluate finite element operators have to be written differently for each target, and by hand that does not scale across the number of element types and polynomial orders a framework like Nektar++ supports. NektarIR takes the high-level description of a finite element operation and compiles it, through MLIR, into kernels specialised for the hardware in front of it. The talk covered matrix-free operators on unstructured three-dimensional meshes with mixed element types, which is the case that matters for real geometries and the one hand-tuning handles worst.

The work is Edward’s Ph.D. topic and is currently under review.