Domain decomposition
In several fields of applied sciences, many problems, that are described by PDEs, lead to the coupling of different mathematical models. For example, fluid-structure interaction problems, coupled electro-mechanical problems, the problem of contacts between bodies or of acoustic wave propagation in heterogeneous media. In such problems, interface conditions between adjacent subdomains have to be taken into account and their efficient implementation plays a key role in the numerical simulation.
One of the interests is focused on the use of non-conforming domain decomposition methods, that allows the use of non-matching grids along the interfaces of the subdomains, where a weak continuity constraint on the solution is imposed. Such approach allows not only to couple different discretizations (such as finite elements, finite differences, spectral elements, wavelets) but also different methods such as domain methods and boundary element methods.
The group's focus is also directed towards the scalability of domain decomposition methods, specifically their efficiency on high-performance computational platforms. Multilevel domain decomposition methods are therefore developed, which combine discretizations on highly refined computational grids with less accurate representations (the so-called "coarse spaces"), with the aim of both improving computational complexity and enhancing convergence robustness with respect to an increasing number of subdomains and/or strongly heterogeneous coefficients.