Fast and Efficient Algorithms in Computational Electromagnetics
Fast and Efficient Algorithms in Computational Electromagnetics
Accelerating Fast Multipole Methods for the Helmholtz Equation at Low Frequencies
IEEE Computational Science & Engineering
Efficient fast multipole method for low-frequency scattering
Journal of Computational Physics
A wideband fast multipole method for the Helmholtz equation in three dimensions
Journal of Computational Physics
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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 larger than one, and becomes six times faster for large multipole orders. The method relies on a connection between the discretizations of the six integral representations, and on the fact that the Wigner D-matrices become diagonal for rotations around the z-axis. The proposed technique can also be extended to the vectorial case in two different ways, one of which is very similar to the scalar case. The other method relies on a Beltrami decomposition of the fields and is faster than the direct approach for any multipole order. This decomposition is also not limited to evanescent wave solvers, but can be used in any vectorial multilevel fast multipole algorithm.