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We introduce high precision finite difference models of the wave equation and Maxwell's equations based on what are called nonstandard (NS) finite differences (FD) for broadband calculation and extensions of NS-FD methodology to solve nonlinear problems.
We first discuss the philosophy of modeling and numerical simulation. Many researchers believe that the more accurate the model – i.e. the better it fits the data – the better. But this is not necessarily true. Besides accuracy, a good model must have the same essential mathematical characteristics as the phenomenon which it is supposed to describe. When this is not the case, a model can be very accurate...
The time-reversed finite difference time domain (FDTD) algorithm is a useful tool for image recovery. By using a negative time step, a scattered wave field can propagated backwards to extract information about the size and shape of a scatterer, but errors, in both the FDTD algorithm and noise in scattered field data, reduce the quality of the recovered image. Using a new high accuracy FDTD algorithm...
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