# BEM FEM methods for PDEs

The group activity is focused on the solution, in the time domain, of some non stationary problems defined in unbounded domains and described by PDEs. In particular, problems whose formulation can be reduced to time-space boundary integral equations are considered. Among the classical examples, it is worth mentioning: the propagation and the simple/multiple scattering of acoustic waves in non viscous fluids, in presence of fixed or rotating obstacles of arbitrary shape; the propagation of elastic (seismic) waves in homogeneous or multilayered media; the propagation of electromagnetic waves. The presence of sources, even located far away from the spatial domain of interest, and of initial data is considered as well.

By using a suitable space-time boundary integral formulation, it is possible to determine the solution of the problem at hand at any desired point. The same integral formulation represents a non reflecting boundary condition that can be defined on an artificial boundary of arbitrary shape, thus allowing to solve the problem on a bounded spatial domain of interest. The solution of the reformulated problem is obtained by coupling a boundary element discretization (BEM) of the above mentioned integral equation with a classical finite element method (FEM) or a finite difference method.