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We present a domain decomposition approach for the computation of the
electromagnetic field within periodic structures. We use a
Schwarz method with transparent boundary conditions at the interfaces of
the domains. Transparent boundary conditions are approximated by the
perfectly matched layer method (PML). To cope with Wood anomalies
appearing in periodic structures an adaptive strategy to determine
optimal PML parameters is developed. \\ We focus on the application to
typical EUV lithography line masks. Light propagation within the
multi-layer stack of the EUV mask is treated analytically. This results
in a drastic reduction of the computational costs and allows for the
simulation of next generation lithography masks
on a standard personal computer.