By using a direct implementation of Maxwell’s curl equations in the time domain, you do little analytical processing of the equations. No vector potential or Green’s functions are developed as in frequency-domain methods. Although the antenna may be volumetrically complex and contain many different materials, the method yields sparse matrices rather than the dense matrices produced by moment methods. It is a direct solution that does not require the inversion of large matrices and includes only nearest-neighbor interactions. Having only nearest-neighbor interactions means that it is possible to run problems on parallel machines.
You need to embed the antenna in a rectangular region and divide it into rectangular cubical cells with sizes ranging from 10 to 20 samples per wavelength at the highest frequency where analysis is desired. The outer surfaces contain absorbing boundaries to eliminate reflections that would produce errors. Formulating absorbing boundary conditions has been a significant part of the method. You need to locate a solution surface between the absorbing boundaries and the antenna outer surface where we compute currents by using the equivalence theorem. The DFT of the time response determines the radiation pattern at a given frequency after the equivalent currents are found. If you need the pattern amplitude in only a few directions, the time-domain radiation can be found directly: for example, the gain in one direction.
We can formulate some problems in one or two dimensions if they possess symmetry instead of the three-dimensional rectangular cube. The solution time is reduced dramatically, and the time-animated presentation may provide sufficient insight when the radiation pattern is found in two dimensions. Because this is a time-domain analysis, we need to excite the structure with a pulse. You use the pulse frequency power response to normalize the patterns and compute gain. When the formulation includes the material losses, the efficiency of the antenna can be found since the dissipation in the inner cells prevents the radiation from reaching the outer surface.
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