A fast algorithm for particle simulations
Journal of Computational Physics
Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
Fast and Efficient Algorithms in Computational Electromagnetics
Fast and Efficient Algorithms in Computational Electromagnetics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A wideband fast multipole method for the Helmholtz equation in three dimensions
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Calderón preconditioning approaches for PMCHWT formulations for Maxwell's equations
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Journal of Computational Physics
Hi-index | 31.46 |
This paper presents an FMM (Fast Multipole Method) for periodic boundary value problems for Maxwell's equations in 3D. The effect of periodicity is taken into account with the help of the periodised moment to local expansion (M2L) transformation formula, which includes lattice sums. We verify the proposed method by comparing the obtained numerical results with analytic solutions for models of the multi-layered dielectric slab. We then apply the proposed method to scattering problems for periodic two-dimensional arrays of dielectric spheres and compare the obtained energy transmittances with those from the previous studies. We also consider scattering problems for woodpile crystals, where we find a passband related to a localised mode. Through these numerical tests we conclude that the proposed method is efficient and accurate.