An accelerated time-domain finite-difference simulation scheme for 3D transient-electromagnetic modeling using multi-grid concepts

Explicit time stepping schemes for the solution of three-dimensional electromagnetic (EM) field simulations have a high computational time demand. The fact that the transient-electromagnetic field is smoothed gradually in space with time allows for a reduced spatial sampling rate of the EM field. Based on concepts known from multi-grid (MG) methods, we have developed a restriction operator in order to map the EM field from a fine to a coarser finite-difference mesh during a forward field simulation. Two advantages follow. First, the grid size can be reduced. Field restriction involves reducing the number of grid nodes by a factor of two 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. The initial simulation grid is identical to the mesh defining the distribution of the electrical conductivity over the model. After field restriction, a material averaging scheme is employed in order to calculate the underlying effective medium on the new (coarse) simulation grid. Test results on the scheme appear quite promising with up to a factor of ten reduction 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. Experiments for an adequate restriction criteria involve a spatial Fourier transform of the EM field to estimate the decay rate of the high frequency contents of the field.