  We investigate a range of techniques for the acceleration of Calder\'on
(operator) preconditioning in the context of boundary integral equation methods
for electromagnetic transmission problems. Our objective is to mitigate as far
as possible the high computational cost of the barycentrically-refined meshes
necessary for the stable discretisation of operator products. Our focus is on
the well-known PMCHWT formulation, but the techniques we introduce can be
applied generically. By using barycentric meshes only for the preconditioner
and not for the original boundary integral operator, we achieve significant
reductions in computational cost by (i) using "reduced" Calder\'on
preconditioners obtained by discarding constituent boundary integral operators
that are not essential for regularisation, and (ii) adopting a "bi-parametric"
approach in which we use a lower quality (cheaper) $\mathcal{H}$-matrix
assembly routine for the preconditioner than for the original operator,
including a novel approach of discarding far-field interactions in the
preconditioner. Using the boundary element software Bempp (www.bempp.com), we
compare the performance of different combinations of these techniques in the
context of scattering by multiple dielectric particles. Applying our
accelerated implementation to 3D electromagnetic scattering by an aggregate
consisting of 8 monomer ice crystals of overall diameter 1cm at 664GHz leads to
a 99% reduction in memory cost and at least a 75% reduction in total
computation time compared to a non-accelerated implementation.
