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Because FDTD is solved by propagating the fields forward in the time ___domain, the electromagnetic time response of the medium must be modeled explicitly. For an arbitrary response, this involves a computationally expensive time convolution, although in most cases the time response of the medium (or [[Dispersion (optics)]]) can be adequately and simply modeled using either the recursive convolution (RC) technique or the auxiliary differential equation (ADE) technique. An alternative way of solving [[Maxwell's equations]] that can treat arbitrary dispersion easily is the Pseudospectral Spatial-Domain method (PSSD), which instead propagates the fields forward in space.
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The most commonly used grid truncation techniques for open-region FDTD modeling problems are the Mür absorbing boundary condition (ABC), the Liao ABC, and various perfectly matched layer (PML) ABC formulations. The Mür and Liao techniques are simpler than PML. However, PML ABCs can provide orders-of-magnitude lower reflections. The PML concept was introduced by J.-P. Berenger in a seminal 1994 paper in the Journal of Computational Physics. Since 1994, Berenger's original split-field implementation has been modified and extended to the uniaxial PML (UPML), the convolutional PML (CPML), and the higher-order PML. The latter two PML formulations have increased ability to absorb evanescent waves, and therefore can in principle be placed closer to a simulated scattering or radiating structure than Berenger's original formulation.
== References ==
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