The behavior laws used in numerical simulations describe the physical characteristics of simulated materials. As our understanding of these materials evolves, the complexity of these laws increases. Integrating these laws is a critical step for the performance and robustness of scientific computations. Therefore, this step can lead to intrusive and complex developments in the code.

Many digital platforms, such as FEniCS, FireDrake, FreeFEM, and Comsol, offer Just-In-Time (JIT) code generation techniques to handle various physics. This JIT approach significantly reduces the time required to implement new simulations, providing great versatility to the user. Additionally, it allows for optimization specific to the cases being treated and facilitates porting to various architectures (CPU or GPU). Finally, this approach hides implementation details; any changes in these details are invisible to the user and absorbed by the code generation layer.

However, these techniques are generally limited to the assembly steps of the linear systems to be solved and do not include the crucial step of integrating behavior laws.

Inspired by the successful experience of the open-source project mgis.fenics [1], this thesis aims to develop a Just-In-Time code generation solution dedicated to the next-generation structural mechanics code Manta [2], developed by CEA. The objective is to enable strong coupling with behavior laws generated by MFront [3], thereby improving the flexibility, performance, and robustness of numerical simulations.

The doctoral student will benefit from guidance from the developers of MFront and Manta (CEA), as well as the developers of the A-Set code (a collaboration between Mines-Paris Tech, Onera, and Safran). This collaboration within a multidisciplinary team will provide a stimulating and enriching environment for the candidate.

Furthermore, the thesis work will be enhanced by the opportunity to participate in conferences and publish articles in peer-reviewed scientific journals, offering national and international visibility to the thesis results.

[1] https://thelfer.github.io/mgis/web/mgis_fenics.html
[2] MANTA : un code HPC généraliste pour la simulation de problèmes complexes en mécanique. https://hal.science/hal-03688160
[3] https://thelfer.github.io/tfel/web/index.html