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The finite-difference frequency-domain method is a numerical solution method for problems usually in electromagnetism and sometimes in acoustics, based on finite-difference approximations of the derivative operators in the differential equation being solved.
While "FDFD" is a generic term describing all frequency-domain finite-difference methods, the title seems to mostly describe the method as applied to scattering problems. The method shares many similarities to the finite-difference time-domain method, so much of the literature on FDTD can be directly applied. The method works by transforming Maxwell's equations for sources and fields at a constant frequency into matrix form A x = b {\displaystyle Ax=b}. The matrix A is derived from the wave equation operator, the column vector x contains the field components, and the column vector b describes the source. The method is capable of incorporating anisotropic materials, but off-diagonal components of the tensor require special treatment.
Strictly speaking, there are at least two categories of "frequency-domain" problems in electromagnetism. One is to find the response to a current density J with a constant frequency ω, i.e. of the form J e i ω t {\displaystyle \mathbf {J} e^{i\omega t}} , or a similar time-harmonic source. This frequency-domain response problem leads to an A x = b {\displaystyle Ax=b} system of linear equations as described above. An early description of a frequency-domain response FDTD method to solve scattering problems was published by Christ and Hartnagel. Another is to find the normal modes of a structure in the absence of sources: in this case the frequency ω is itself a variable, and one obtains an eigenproblem A x = λ x {\displaystyle Ax=\lambda x} . An early description of an FDTD method to solve electromagnetic eigenproblems was published by Albani and Bernardi.