Romain Mottier: Thursday, 17th July 2025 – 10h30 to 12h00
Abstract:
The objective of this Thesis is to develop approximation methods for the simulation of elasto-acoustic wave propagation. The spatial discretization of these equations relies on Hybrid High-Order (HHO) methods, which offer several advantageous properties, such as the ability to handle general meshes, computational efficiency, and high accuracy. An energy-norm error estimate is derived in the space semi-discrete setting. The time discretization is based on Runge–Kutta schemes. Particular attention is given to the stability of explicit schemes and to the efficiency of both explicit and implicit approaches. Numerical results are presented, including a geophysical application involving a complex geometry and strong heterogeneities. A second important aspect explored in this Thesis concerns the use of so-called unfitted meshes for elliptic problems with curved interfaces. These meshes do not conform to the physical interfaces, leading to mesh cells that may be intersected by them. This approach simplifies the mesh design. A method based on polynomial extension is introduced and analyzed in order to handle ill-cut cells. This approach is less intrusive than the more classical one based on the agglomeration of ill-cut cells.
