Quadrature by Parity Asymptotic eXpansions (QPAX) for scattering by high aspect ratio particles

@article{Carvalho2021QuadratureBP,
  title={Quadrature by Parity Asymptotic eXpansions (QPAX) for scattering by high aspect ratio particles},
  author={Camille Carvalho and Arnold D. Kim and Lori Lewis and Zois Moitier},
  journal={ArXiv},
  year={2021},
  volume={abs/2105.02136}
}
We study scattering by a high aspect ratio particle using boundary integral equation methods. This problem has important applications in nanophotonics problems, including sensing and plasmonic imaging. Specifically, we consider scattering in two dimensions by a sound-hard, high aspect ratio ellipse. For this problem, we find that the boundary integral operator is nearly singular due to the collapsing geometry from an ellipse to a line segment. We show that this nearly singular behavior leads to… 

Figures from this paper

References

SHOWING 1-10 OF 29 REFERENCES

Asymptotic analysis for close evaluation of layer potentials

Highly accurate special quadrature methods for Stokesian particle suspensions in confined geometries

TLDR
This article presents a boundary integral method that can be used to study the motion of rigid particles in three‐dimensional periodic Stokes flow with confining walls, based on a combination of upsampled quadratures and quadrature by expansion, accelerated using a precomputation scheme.

Asymptotic Approximations for the Close Evaluation of Double-Layer Potentials

TLDR
This work derives the asymptotic approximation for the case of the double-layer potential in two and three dimensions, representing the solution of the interior Dirichlet problem for Laplace's equation.

Slender-body theory for plasmonic resonance

TLDR
A slender-body theory for plasmonic resonance of slender metallic nanoparticles, focusing on a general class of axisymmetric geometries with locally paraboloidal tips, is developed and it is shown that the permittivity eigenvalues of the axisymetric modes are strongly singular in the slenderness parameter, implying widely tunable, high-quality-factor, resonances in the near-infrared regime.

On the evaluation of layer potentials close to their sources

On the Numerical Evaluation of Electrostatic Fields in Dense Random Dispersions of Cylinders

TLDR
A new integral equation method is presented for the solution of the interface problem which uses a recently developed method of images to resolve the close-to-touching interactions and the fast multipole method to compute far field interactions.

The fast Fourier transform and the numerical solution of one-dimensional boundary integral equations

SummaryHere we present a fully discretized projection method with Fourier series which is based on a modification of the fast Fourier transform. The method is applied to systems of

A Simple Method for Computing Singular or Nearly Singular Integrals on Closed Surfaces

We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near