An accelerated time domain finite difference simulation scheme for three-dimensional transient electromagnetic modeling using geometric multigrid concepts

[ 1] The fact that the transient electromagnetic (TEM) field is smoothed gradually in space with time allows for a reduced spatial sampling rate of the EM field. On the basis of concepts known from multigrid methods, we have developed a restriction operator in order to map the EM field and the material properties from a fine to a coarser finite difference mesh during a forward field simulation with an explicit time-stepping scheme. Two advantages follow. First, the grid size can be reduced. Field restriction involves reducing the number of grid nodes by a factor of 2 for each Cartesian direction. Second, as can be seen from the Courant-Friedrichs-Levy condition, the larger grid spacing allows for proportionally larger time step sizes. After field restriction, a material averaging scheme is employed in order to calculate the underlying effective medium on the coarse simulation grid. Example results show a factor of up to 5 decrease in solution run time, compared to a scheme that uses a constant grid. Key to the accuracy of the approach is knowledge of the proper time range to restrict the fields. An adequate criterion to decide during run time when to restrict involves an error measure for the locations of interest between the fields on the fine mesh and the restricted fields.