  We introduce multilayer structures with the phase-change material
Ge$_2$Sb$_2$Te$_5$ (GST) for use as broadband switchable absorbers in the
infrared wavelength range. We optimize both the material composition and the
layer thicknesses of the multilayer structures, in order to maximize the
difference between the absorption for GST in its crystalline phase and the
absorption for GST in its amorphous phase in the wavelength range of interest.
We show that in the optimized structures near perfect absorption can be
switched to very low absorption in a broad wavelength range by switching GST
from its crystalline to its amorphous phase. Our optimized lithography-free
structures have better performance than harder-to-fabricate three-dimensional
structures. Our results could pave the way to a new class of broadband
switchable absorbers and thermal sources in the infrared wavelength range.
