PhD Position F/M Mesh partitioning for high performance solvers on Exascale computing systems

About this position

This PhD will be part of the Horizon Europe HORIZON-JU-EUROHPC-2026-COE-LH-01-03 FEniCS Lighthouse project, which is fully funded and will start in January 2027. The other international partners of the project are Simula Research Laboratory, Norway; University of Cambridge Cambridge, United Kingdom; University College London, United Kingdom; University of Luxembourg, Luxembourg; Koç University, Türkiye; Sabancı University, Türkiye. The PhD will work closely with the researchers in this project.

Real-world applications of finite element mesh (FEM) simulations require parallel computing.In such a setting, computational meshes must be partitioned among multiple computers as a first step. One important goal of mesh partitioning is to keep the resulting inter-process communication overhead low while achieving load balance. Failing to do so will lead to parallel FEM simulations which do not scale.

The current state-of-the-art and mainstream approaches treat mesh partitioning as a graph or hypergraph partitioning problem, which is then tackled with well-known libraries. The common goal of these libraries is to minimize the total volume of inter-process communication. However, this does not accurately reflect the inter-process communication cost in the current systems.

This mismatch is exacerbated specifically on today’s strongly hierarchical HPC topologies, which have highly variable inter-process communication cost. The current mesh partitioner needs major improvements to incorporate the proper objectives in its underlying optimization procedures, and thus achieve scalable finite element computations on current and future supercomputers. This PhD will work to develop a novel approach to mesh/graph/hypergraph partitioning by adopting an optimization objective that truly reflects the actual communication overhead.

The PhD will design, analyze, and implement algorithms for mesh partitioning and collaborate with the project partners to make use of it in the open source FEniCS framework

https://fenicsproject.org.

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