  This work presents a fast direct solver strategy for electromagnetic integral
equations in the high-frequency regime. The new scheme relies on a suitably
preconditioned combined field formulation and results in a single skeleton form
plus identity equation. This is obtained after a regularization of the elliptic
spectrum through the extraction of a suitably chosen equivalent circulant
problem. The inverse of the system matrix is then obtained by leveraging the
Woodbury matrix identity, the low-rank representation of the extracted part of
the operator, and fast circulant algebra yielding a scheme with a favorable
complexity and suitable for the solution of multiple right-hand sides.
Theoretical considerations are accompanied by numerical results both of which
are confirming and showing the practical relevance of the newly developed
scheme.
