26 research outputs found
Fourier Based Fast Multipole Method for the Helmholtz Equation
The fast multipole method (FMM) has had great success in reducing the
computational complexity of solving the boundary integral form of the Helmholtz
equation. We present a formulation of the Helmholtz FMM that uses Fourier basis
functions rather than spherical harmonics. By modifying the transfer function
in the precomputation stage of the FMM, time-critical stages of the algorithm
are accelerated by causing the interpolation operators to become
straightforward applications of fast Fourier transforms, retaining the
diagonality of the transfer function, and providing a simplified error
analysis. Using Fourier analysis, constructive algorithms are derived to a
priori determine an integration quadrature for a given error tolerance. Sharp
error bounds are derived and verified numerically. Various optimizations are
considered to reduce the number of quadrature points and reduce the cost of
computing the transfer function.Comment: 24 pages, 13 figure
Two-Step lagrange interpolation method for the multilevel fast multipole algorithm
Cataloged from PDF version of article.We present a two-step Lagrange interpolation method for the efficient solution of large-scale electromagnetics problems with the multilevel fast multipole algorithm (MLFMA). Local interpolations are required during aggregation and disaggregation stages of MLFMA in order to match the different sampling rates for the radiated and incoming fields in consecutive levels. The conventional one-step method is decomposed into two one-dimensional interpolations, applied successively. As it provides a significant acceleration in processing time, the proposed two-step method is especially useful for problems involving large-scale objects discretized with millions of unknowns. © 2006 IEEE
Two-Step lagrange interpolation method for the multilevel fast multipole algorithm
We present a two-step Lagrange interpolation method for the efficient solution of large-scale electromagnetics problems with the multilevel fast multipole algorithm (MLFMA). Local interpolations are required during aggregation and disaggregation stages of MLFMA in order to match the different sampling rates for the radiated and incoming fields in consecutive levels. The conventional one-step method is decomposed into two one-dimensional interpolations, applied successively. As it provides a significant acceleration in processing time, the proposed two-step method is especially useful for problems involving large-scale objects discretized with millions of unknowns. © 2006 IEEE
Towards a scalable parallel MLFMA in three dimensions
The development of a scalable parallel multilevel fast multipole algorithm (MLFMA) for three dimensional electromagnetic scattering problems is reported. In the context of this work, the term 'scalable' denotes the ability to handle larger simulations with a proportional increase in the number of parallel processes (CPU cores), without loss of parallel efficiency. The workload is divided among the different processes according to the hierarchical partitioning scheme. Crucial to ensure the parallel scalability of the algorithm, is that the radiation patterns - sampled on the sphere - are partitioned in two dimensions, i.e., both in azimuth and elevation directions
A fast 2-D parallel multilevel fast multipole algorithm solver for oblique plane wave incidence
We present a multilevel fast multipole algorithm (MLFMA) implementation to numerically solve Maxwell's equations for large two-dimensional geometries illuminated by an arbitrary plane wave in three-dimensional space. The solver's capabilities are augmented by means of an asynchronous and hierarchical parallelization. Its accuracy is demonstrated by comparing the analytical and numerically obtained scattering width of several canonical examples with a size of 700,000 wavelengths