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Computing the Casimir force and energy between objects is a classical problemof quantum theory going back to the 1940s. Several different approaches havebeen developed in the literature often based on different physical principles.Most notably a representation of the Casimir energy in terms of determinants ofboundary layer operators makes it accessible to a numerical approach. In thispaper, we first give an overview of the various methods and discuss theconnection to the Krein-spectral shift function and computational aspects. Wepropose variants of Krylov subspace methods for the computation of the Casimirenergy for large-scale problems and demonstrate Casimir computations forseveral complex configurations. This allows for Casimir energy calculation forlarge-scale practical problems and significantly speeds up the computations inthat case.

Numerical aspects of Casimir energy computation in acoustic scattering