Abstract-This letter reports the initial application of a geodesic finite-difference time-domain (FDTD) grid to model impulsive extremely low frequency electromagnetic wave propagation about the Earth sphere. The two-dimensional transverse-magnetic grid is comprised entirely of hexagonal cells, except for a small fixed number of pentagonal cells needed for grid completion. Grid-cell areas and locations are optimized to yield a smoothly varying area difference between adjacent cells, thereby maximizing numerical convergence. The new FDTD grid model is considerably superior to our previously reported latitude-longitude grid because it is simpler to construct, avoids geometrical singularities at the poles, executes about 14 times faster, provides much more isotropic wave propagation, and permits an easier interchange of data with state-of-the-art Earth-simulation codes used by the geophysics community. We verify our new model by conducting numerical studies of impulsive antipodal propagation and the Schumann resonance.

The design of metal microelectrodes that produce minimal damage to tissue and can successfully record from and stimulate targeted neural structures necessitates a thorough understanding of the electrical phenomena generated in the tissue surrounding the electrodes. Computational modeling has been a primary strategy used to study these phenomena, and the Finite Element Method has proven to be a powerful approach. Much research has been directed toward the development of models for electrode recording and stimulation, but very few models reported in the literature thus far incorporate the effects of the electrode-electrolyte interface, which can be a source of very high impedance, and thus likely a key component of the system.To explore the effects that the electrode-electrolyte interface has upon the electric potential and current density surrounding metal microelectrodes, simulations of electrodesaline systems in which the electrodes were driven at AC potentials ranging from 10 mV to 500 mV and frequencies of 100 Hz to 10 kHz have been performed using the Finite Element Method. Solutions obtained using the thin layer approximation for the electrode-electrolyte interface were compared with those generated using a thin uniform layer, a representation that has previously appeared in the literature. Solutions using these two methods were similar in the linear regime of the interface, however, the thin layer approximation has important advantages over its competitor including ease of application and low computational cost.

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