  We present a generalisation of efficient numerical frameworks for modelling
fluid-filament interactions via the discretisation of a recently-developed,
non-local integral equation formulation to incorporate regularised Stokeslets
with half-space boundary conditions, as motivated by the importance of
confining geometries in many applications. We proceed to utilise this framework
to examine the drag on slender inextensible filaments moving near a boundary,
firstly with a relatively-simple example, evaluating the accuracy of resistive
force theories near boundaries using regularised Stokeslet segments. This
highlights that resistive force theories do not accurately quantify filament
dynamics in a range of circumstances, even with analytical corrections for the
boundary. However, there is the notable and important exception of movement in
a plane parallel to the boundary, where accuracy is maintained. In particular,
this justifies the judicious use of resistive force theories in examining the
mechanics of filaments and monoflagellate microswimmers with planar flagellar
patterns moving parallel to boundaries. We proceed to apply the numerical
framework developed here to consider how filament elastohydrodynamics can
impact drag near a boundary, analysing in detail the complex responses of a
passive cantilevered filament to an oscillatory flow. In particular, we
document the emergence of an asymmetric periodic beating in passive filaments
in particular parameter regimes, which are remarkably similar to the power and
reverse strokes exhibited by motile 9+2 cilia. Furthermore, these changes in
the morphology of the filament beating, arising from the fluid-structure
interactions, also induce a significant increase in the hydrodynamic drag of
the filament.
