Two-Step Lagrange Interpolation Method for the Multilevel Fast Multipole Algorithm

Efficient Preconditioning Strategies for the Multilevel Fast Multipole Algorithm

For the iterative solutions of the integral equation methods employing the multilevel fast multipole algorithm (MLFMA), effective preconditioning techniques should be developed for robustness and efficiency. Preconditioning techniques for such problems can be broadly classified as fixed preconditioners that are generated from the sparse near-field matrix and variable ones that can make use of M...

Lagrange Two-Dimensional Interpolation Method for Modeling Nanoparticle Formation During RESS Process

Using Fast Fourier Transform in the 3-d Multilevel Fast Multipole Algorithm

In this paper a method is presented how to perform interpolation and anterpolation in both spherical coordinates θ and φ by trigonometric polynomials and the fast Fourier transform (FFT) in the 3-D multilevel fast multipole algorithm (MLFMA). The proposed method is exact in interpolation and anterpolation, and has the high numerical efficiency of FFT. A numerical comparison suggests that the pr...

Functional Algorithm Simulation of the Fast Multipole Method: Architectural Implications

Functional Algorithm Simulation is a methodology for predicting the computation and communication characteristics of parallel algorithms for a class of scientiic problems, without actually performing the expensive numerical computations involved. In this paper, we use Functional Algorithm Simulation to study the parallel Fast Multipole Method (FMM), which solves the N-body problem. Functional A...

Fast and accurate analysis of large-scale composite structures with the parallel multilevel fast multipole algorithm.

Accurate electromagnetic modeling of complicated optical structures poses several challenges. Optical metamaterial and plasmonic structures are composed of multiple coexisting dielectric and/or conducting parts. Such composite structures may possess diverse values of conductivities and dielectric constants, including negative permittivity and permeability. Further challenges are the large sizes...