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.
The interest 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.