  Direct solvers are a common method for solving finite difference frequency
domain (FDFD) systems that arise in numerical solutions of Maxwell's equations.
In a direct solver, one factorizes the system matrix. Since the system matrix
is typically very sparse, the fill-in of these factors is the single most
important computational consideration in terms of time complexity and memory
requirements. As a result, it is of great interest to determine ways in which
this fill-in can be systematically reduced. In this paper, we show that in the
context of commonly used perfectly matched boundary layer methods, the choice
of boundary condition behind the perfectly matched boundary layer can be
exploited to reduce fill-in incurred during the factorization, leading to
significant gains of up to 40 percent in the efficiency of the factorization
procedure. We illustrate our findings by solving linear systems and eigenvalue
problems associated with the FDFD method.
