Section: Research Program

Integral equations

Our activity in this field aims at developing accurate and fast methods for 3D acoustic and elastodynamic problems based on the discretization of boundary integral equations.

In traditional implementation, the dimensional advantage of Boundary Element Methods (BEM) with respect to domain discretization methods is offset by the fully-populated nature of the BEM matrix. Various approaches such as the Fast Multipole Method (FMM) or hierarchical matrices (H-matrices) have been proposed to overcome this drawback and derive fast BEMs. The specificity of our work consists in deriving such approaches not only for 3D acoustic wave propagation but also for 3D elastodynamics with applications in soil-structure interaction, seismology or seismic imaging.

Since the solution is computed through an iterative solver, a crucial point is then to control the number of iterations as the problem complexity increases, through the development of adapted preconditioners.

Besides, we also try to hybridize integral equations and high-frequency methods for scattering problems ,in order to tackle configurations with scatterers of different size-scales, compared to the wavelength.

Finally, we have studied the relationship between the Maxwell and eddy current models for three-dimensional configurations involving highly-conducting bounded bodies in air and sources placed remotely from those bodies