École Nationale Supérieure de
Techniques Avancées

Résumé

This report presents the work that I conducted during a research internship at the Max Planck Institute for Plasma Physics in the Numerical Methods for Plasma Physics department. This report is focusing on the implementation and validation of solid mechanics equations using Psydac, a finite element library in Python. The primary objective of my internship was to explore and extend Psydac's capabilities to solve partial differential equations from solid mechanics, which had not been previously tested in this library. The work focused on two main areas: linear elasticity and stationary thermoelasticity problems and their execution on a supercomputer. For linear elasticity, two formulations, pure displacement and mixed displacement-pressure formulations, were implemented and analyzed. The thermoelasticity study involved solving coupled thermo-mechanical problems on composite materials with spatially varying properties. This work required the development of enhanced discretization capabilities, including the implementation of custom grid discretization features to handle material property discontinuities. Additionally, a multipatch framework was explored to address complex geometries with holes, utilizing Nitsche's method for interface coupling. All simulations were performed on the supercomputer Raven, which is maintained by the Max Planck Computing and Data Facility. These results have been used to verify the implementation and the effectiveness of Psydac to solve solid mechanics problems.