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# Finite-difference frequency-domain

The finite-difference frequency-domain (FDFD) is a numerical solution for problems usually in electromagnetism. The method is, of course, 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 (or other partial differential equation) into matrix form [A] [x] = [b] . The matrix [A] is the wave equation operator, the column vector [x] contains the field components, and the column vector [b] describes the source.

FDFD is arguably the simplest numerical method to implement to solve Maxwell's equations. The method does little to minimize the size of the matrices it produces so it tends to be less efficient than techniques like the finite element method. It resolves the field throughout a volume so it is an excellent technique for modeling devices with high volumetric complexity or visualizing the fields. For 2D simulations, it is capable of modeling finite sized devices or complicated waveguide discontinuity problems.

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Tips for Implementing the Method

1. Use a Yee grid as this implicitly satisfies the zero divergence conditions to avoid spurious solutions.

2. Much of the literature on finite-difference time-domain (FDTD) applies to FDFD, particularly topics on how to represent materials and devices on a Yee grid.

Literature

See Chapter 3 in... [http://purl.fcla.edu/fcla/etd/CFE0001159]

ee also

Finite-difference time-domain method

* [http://ab-initio.mit.edu/wiki/index.php/MPB_Introduction MPB Introduction: Comparison of FDTD and FDFD]

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