  Within the scattering theoretical approach, the Casimir force is obtained
numerically by an evaluation of the round trip of an electromagnetic wave
between the objects involved. Recently [Hartmann M et al. 2017, Phys. Rev.
Lett. 119 043901] it was shown that a symmetrization of the scattering operator
provides significant advantages for the numerical evaluation of the Casimir
force in the experimentally relevant sphere-plane geometry. Here, we discuss in
more detail how the symmetrization modifies the scattering matrix in the
multipole basis and how computational time is reduced. As an application, we
discuss how the Casimir force in the sphere-plane geometry deviates from the
proximity force approximation as a function of the geometric parameters.
