Scattering Approach to Casimir Force
Casimir force between multiple objects of different shapes and material properties can be related to scattering amplitudes of electromagnetic fields from individual bodies.
"Scattering theory approach to electrodynamic Casimir forces,"
S.J. Rahi, T. Emig, N. Graham, R.L. Jaffe, and M. Kardar, Phys. Rev. D 80, 085021 (2009)
Shapes amenable to exact treatment of electromagnetic scattering:
Plane, sphere, cylinder (circular, parabolic, elliptic), wedge, cone, ...