Error measures for comparing bioelectromagnetic simulators

FDTD vs. AIM for bioelectromagnetic analysis

“…The AIM parameters are optimized as described in [5]; it~3 00 N for all simulations; and a parallel implementation of the method is used for the simulations [5] and all computational costs are 'serialized' by multiplying the number of processes used for the simulation with the observed wall-clock time and the maximum memory used among all the processes. The errors are quantified by comparing the results to reference Mie series solutions using the norms described in [7]; specifically, the relative error for the total time-average absorbed power and the L2 error norm for the electric field are computed. These are the norms in [7] that are the least and most sensitive to phase and direction errors in the computed electric field, respectively; as such, they are expected to over-and under-estimate the utility of the simulations.…”

“…The errors are quantified by comparing the results to reference Mie series solutions using the norms described in [7]; specifically, the relative error for the total time-average absorbed power and the L2 error norm for the electric field are computed. These are the norms in [7] that are the least and most sensitive to phase and direction errors in the computed electric field, respectively; as such, they are expected to over-and under-estimate the utility of the simulations.…”

“…To compare the errors and costs of the methods, two sets of inhomogeneous multilayered voxel-based and CAD models of spherical head and leg phantoms are utilized as benchmark problems [7]. The scaterred fields are computed at 900 MHz: Each structure is excited by an x-polarized unit plane-wave propagating in the -z direction for AIM simulations; for FDTD simulations, a similarly polarized modulated Gaussian pulse is used; the carrier frequency and bandwidth of the pulse are increased from 600 MHz 400 MHz ∓ to 1.8 GHz ∓ 1.6 GHz [8] as the mesh size decreases so that t~3 000 N in all cases.…”

An FFT-Accelerated Integral-Equation Solver for Analyzing Scattering in Rectangular Cavities

“…The steak model is centered in the middle of the cavity and is excited by an impressed unit electric Hertzian dipole that is located at (0.1 m, 0.21 m, 0.175 m) and points in the direction (other excitations for this cavity are considered in Section III-C). The accuracy of the simulations are quantified by computing the time-average absorbed power density and finding the L1 relative error norm [45] (26) The MOM solution of the same problem is used as reference when feasible; otherwise, a more accurate AIM solution is used (fifth-order moments are matched and ). The AIM parameters are chosen to minimize the computational costs subject to the constraint that ; these parameters are detailed in Table I.…”