  Computing the Casimir force and energy between objects is a classical problem
of quantum theory going back to the 1940s. Several different approaches have
been developed in the literature often based on different physical principles.
Most notably a representation of the Casimir energy in terms of determinants of
boundary layer operators makes it accessible to a numerical approach. In this
paper, we first give an overview of the various methods and discuss the
connection to the Krein-spectral shift function and computational aspects. We
propose variants of Krylov subspace methods for the computation of the Casimir
energy for large-scale problems and demonstrate Casimir computations for
several complex configurations. This allows for Casimir energy calculation for
large-scale practical problems and significantly speeds up the computations in
that case.
