  Computational methods for electromagnetic and light scattering can be used
for the calculation of optical forces and torques. Since typical particles that
are optically trapped or manipulated are on the order of the wavelength in
size, approximate methods such as geometric optics or Rayleigh scattering are
inapplicable, and solution or either the Maxwell equations or the vector
Helmholtz equation must be resorted to. Traditionally, such solutions were only
feasible for the simplest geometries; modern computational power enable the
rapid solution of more general--but still simple--geometries such as
axisymmetric, homogeneous, and isotropic scatterers. However, optically-driven
micromachines necessarily require more complex geometries, and their
computational modelling thus remains in the realm of challenging computational
problems. We review our progress towards efficient computational modelling of
optical tweezers and micromanipulation, including the trapping and manipulation
of complex structures such as optical micromachines. In particular, we consider
the exploitation of symmetry in the modelling of such devices.
