Exascale supercomputers are based on heterogeneous architectures that combine CPUs and GPUs, making it necessary to redesign numerical algorithms to fully exploit all available resources. In large-scale finite element simulations, the solution of linear systems using iterative solvers and algebraic multigrid (AMG) preconditioners remains a major performance bottleneck.

The objective of this PhD is to study and develop hybrid preconditioning strategies adapted to such heterogeneous systems. The work will investigate how multilevel and AMG techniques can be structured to efficiently use both CPUs and GPUs, without restricting computations to a single type of processor. Particular attention will be paid to data distribution, task placement, and CPU–GPU interactions within multilevel solvers.

From a numerical point of view, the research will focus on the analysis and construction of multilevel operators, including grid hierarchies, intergrid transfer operators, and smoothing procedures on avalible GPU's and CPU's. The impact of these choices on convergence, spectral properties, and robustness of preconditioned iterative methods will be studied. Mathematical criteria guiding the design of efficient hybrid preconditioners will be investigated and validated on representative finite element problems, e.g., regional-scale earthquake analysis.

These developments will be coupled with domain decomposition and parallelization strategies adapted to heterogeneous architectures. Particular attention will be paid to CPU–GPU data transfers, memory usage, and the balance between compute-bound and memory-bound kernels. The interaction between numerical choices and hardware constraints, such as CPU and GPU memory hierarchies, will be designed and developed to ensure scalable and efficient implementations.