This paper introduces a general multigrid-subgridding formulation aimed at improving the efficiency of the transmission line matrix method. The rigorous algebraic procedure, based on Hilbert space formulation, leads to the definition of a general boundary scattering matrix, which interfaces 3-D regions of uniform computational mesh with different spatial resolution, thus allowing the modeling of objects of very disparate geometrical or electrical scale, e.g., such occurring in nanodevices. Computational acceleration and accuracy are measured by comparing the run time of simulations performed with subgridding to the run time of simulations without any subgridding.
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