Multiphysics computing is becoming increasingly important for solving problems of major interest in almost all technical fields of research & development and advanced design. Reliability of these computational predictions for complex systems requires that the preponderant couplings are taken into account. An application at the core of the thesis scope pertains to severe accidents in nuclear reactors. In this context, so-called "scenario" codes are used to represent the temporal and spatial sequence of a severe accident involving many coupled-event models, with different levels of discretization depending on the requirement for each physics considered. The key point for the proposed work, common to a large number of multiphysics approaches, is the construction in the solution process of a coupling graph whose nodes of very heterogeneous size and numerical cost are the connected models. The traversal of such graphs on parallel architectures is very crucial to preserve the global solution performance and fully exploits the parallel capabilities of the different coupled tools taken individually, when the size of the models they process naturally justifies it. This numerical performance is crucial to make multiphysics analyses relevant. Indeed, the increase in the complexity of the treated systems comes with an increase in the uncertainties on the models and the data; accordingly, any solution needs to be given with a statistical uncertainty obtained via a large number of solutions.

Within the framework of the thesis, the coupling graphs to be considered are dynamic in the sense that the models associated with each node can appear or vanish, and launch events at certain times that may require synchronization. The graphs can be large and include nodes associated with a lumped-parameter model that is very fast to compute, models composed of ordinary and/or algebraic differential equations, reduced models (including neural networks), up to highly meshed and numerically expensive distributed parameter models. The main objective will then be to optimize the heterogeneous graph traversal in terms of numerical accuracy, computational time, parallel performance and load balancing. The management of the time synchronization on the events launched by the nodes is also a subject of optimization in this context. As previously introduced, a secondary objective of the thesis will be the use of the coupling graph in the framework of statistical studies based on dynamic event trees in order to allow the propagation and evaluation of uncertainties in the multiphysics simulations considered. Considering multiple resolutions in the process of optimization of numerical performance may then be of particular interest.

In practice, the PhD thesis will involve elements of graph theory, numerical analysis methods for time coupling and stability of numerical schemes and software engineering by the development in scientific computational tools. The work will be promoted through publications and participation in international conferences in the field of applied mathematics and scientific computing. This will allow the PhD student to exchange with foreign researchers and/or to share his experience with experts, in the same field and outside. He will also benefit from the network and the scientific environment offered by the CEA laboratory, expert in the field of severe accidents modelling, and will also be in contact via the thesis director with the AVALON team at INRIA, expert in mathematical and computer methods for parallel computing.