Numerical dispersion control in discrete wave simulations in electrically large structures using spectral elements

Domain decomposition techniques have been proposed previously for the modeling of EM wave interactions with electrically large structures. One specific domain decomposition approach splits the structure into smaller regions in which numerical solutions are computed separately with "basis" excitations on the partitions between the regions. Then, field continuity at the partitions is invoked to obtain the solution in the entire structure subject to a specific excitation. The key merits of such an approach are: a) its inherent parallelism, making it ideal for implementation on massively parallel machines; and b) the fact that the solutions in each region can be developed using the most suitable numerical technique. Unfortunately, it can be shown that for those regions for which finite element techniques are required, the numerical discretization needs to use a number of nodes per wavelength dictated by the electrical size of the entire structure in order to keep numerical dispersion at a minimum. In an attempt to deal with this issue, the author examines the advantages that the so-called spectral methods offer in improving the accuracy of differential-equation based wave simulations.