The numerical solution of wave-propagation and scattering problems
typically presents a variety of significant challenges: these problems
require high discretization densities and often give rise to poorly
conditioned numerics. Realistic engineering configurations, further,
usually require consideration of geometries of great complexity and
large extent - including, possibly, singular elements such as wires,
corners, edges and open screens. In this talk we will consider a
number of theoretical aspects concerning these problems as well as
associated computational methodologies that effectively address the
difficulties entailed.