Comparison of Electromagnetic Forces Evaluated in Yee-Lattice Finite-Difference Time-Domain and Lattice-Boltzmann Method

Abstract

Electrodynamic simulations in the Yee-lattice finite-difference time-domain method (YL-FDTDM) require half-unit-cell and half-time-unit offsets between electric and magnetic field components. To evaluate energy, momentum, and force in the YL-FDTDM, electric and magnetic fields must be colocated in both space and time. Colocation operations can be computationally intensive while introducing implementation complexity and numerical error. As an alternative to the YL-FDTDM, the Hauser and Verhey electrodynamic lattice-Boltzmann method (HV ELBM) is implemented on a single lattice representing electric and magnetic fields at the same location and time. Since colocation is not required on a single lattice, its central differences are simpler to implement and more accurate. Continuous plane-wave scattering of electric and magnetic fields from a nondispersive dielectric sphere is solved using the YL-FDTDM, the HV ELBM, and Mie scattering analysis. The YL-FDTDM and HV ELBM are compared in terms of numerical error and computational time representing the analytical Mie solution for the Einstein and Laub time-averaged force density. The HV ELBM requires less computational time to evaluate a time-averaged force density with half the error of the YL-FDTDM. At a similar absolute error, the HV ELBM evaluates a time-averaged force density in less than 10% of the computational time.