Alternative Tilings for the Fast Multipole Method on the Plane

A Comparative Study of Multipole and Empirical Relations Methods for Effective Index and Dispersion Calculations of Silica-Based Photonic Crystal Fibers

In this paper, we present a solid-core Silica-based photonic crystal fiber (PCF) composed of hexagonal lattice of air-holes and calculate the effective index and chromatic dispersion of PCF for different physical parameters using the empirical relations method (ERM). These results are compared with the data obtained from the conventional multipole method (MPM). Our simulation results reveal tha...

Improved Interpolation of Evanescent Plane Waves for Fast Multipole Methods

One way to implement a low-frequency or broadband fast multipole method is to use the spectral representation, or inhomogeneous plane-wave expansion, of the Green’s function. To significantly improve the error-controllability of the method, we propose a new interpolation and anterpolation scheme for the evanescent part. DOI: 10.2529/PIERS060907051636 The fast multipole method (FMM) can be used ...

A faster aggregation for 3D fast evanescent wave solvers using rotations

A novel technique to accelerate the aggregation and disaggregation stages in evanescent plane wave methods is presented. The new method calculates the six plane wave radiation patterns from a multipole expansion (aggregation) and calculates the multipole expansion of an incoming field from the six plane wave incoming field patterns. It is faster than the direct approach for multipole orders lar...

Efficient fast multipole method for low-frequency scattering

The solution of the Helmholtz and Maxwell equations using integral formulations requires to solve large complex linear systems. A direct solution of those problems using a Gauss elimination is practical only for very small systems with few unknowns. The use of an iterative method such as GMRES can reduce the computational expense. Most of the expense is then computing large complex matrix vecto...

Error Control of the Vectorial Nondirective Stable Plane Wave Multilevel Fast Multipole Algorithm