### Abstract

Fast, high-accuracy algorithms for electromagnetic scattering from axisymmetric objects are of great importance when modeling physical phenomena in optics, materials science (e.g. meta-materials), and many other fields of applied science. In this paper, we develop an FFT-accelerated separation of variables solver that can be used to efficiently invert integral equation formulations of Maxwell's equations for scattering from axisymmetric penetrable (dielectric) bodies. Using a standard variant of Müller's integral representation of the fields, our numerical solver rapidly and directly inverts the resulting second-kind integral equation. In particular, the algorithm of this work (1) rapidly evaluates the modal Green's functions, and their derivatives, via kernel splitting and the use of novel recursion formulas, (2) discretizes the underlying integral equation using generalized Gaussian quadratures on adaptive meshes, and (3) is applicable to geometries containing edges and points. Several numerical examples are provided to demonstrate the efficiency and accuracy of the aforementioned algorithm in various geometries.

Original language | English (US) |
---|---|

Pages (from-to) | 152-174 |

Number of pages | 23 |

Journal | Journal of Computational Physics |

Volume | 390 |

DOIs | |

State | Published - Aug 1 2019 |

### Fingerprint

### Keywords

- Body of revolution
- Dielectric media
- Electromagnetics
- Fast Fourier transform
- Müller's integral equation
- Penetrable media

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)
- Computer Science Applications

### Cite this

**An FFT-accelerated direct solver for electromagnetic scattering from penetrable axisymmetric objects.** / Lai, Jun; O'Neil, Michael.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - An FFT-accelerated direct solver for electromagnetic scattering from penetrable axisymmetric objects

AU - Lai, Jun

AU - O'Neil, Michael

PY - 2019/8/1

Y1 - 2019/8/1

N2 - Fast, high-accuracy algorithms for electromagnetic scattering from axisymmetric objects are of great importance when modeling physical phenomena in optics, materials science (e.g. meta-materials), and many other fields of applied science. In this paper, we develop an FFT-accelerated separation of variables solver that can be used to efficiently invert integral equation formulations of Maxwell's equations for scattering from axisymmetric penetrable (dielectric) bodies. Using a standard variant of Müller's integral representation of the fields, our numerical solver rapidly and directly inverts the resulting second-kind integral equation. In particular, the algorithm of this work (1) rapidly evaluates the modal Green's functions, and their derivatives, via kernel splitting and the use of novel recursion formulas, (2) discretizes the underlying integral equation using generalized Gaussian quadratures on adaptive meshes, and (3) is applicable to geometries containing edges and points. Several numerical examples are provided to demonstrate the efficiency and accuracy of the aforementioned algorithm in various geometries.

AB - Fast, high-accuracy algorithms for electromagnetic scattering from axisymmetric objects are of great importance when modeling physical phenomena in optics, materials science (e.g. meta-materials), and many other fields of applied science. In this paper, we develop an FFT-accelerated separation of variables solver that can be used to efficiently invert integral equation formulations of Maxwell's equations for scattering from axisymmetric penetrable (dielectric) bodies. Using a standard variant of Müller's integral representation of the fields, our numerical solver rapidly and directly inverts the resulting second-kind integral equation. In particular, the algorithm of this work (1) rapidly evaluates the modal Green's functions, and their derivatives, via kernel splitting and the use of novel recursion formulas, (2) discretizes the underlying integral equation using generalized Gaussian quadratures on adaptive meshes, and (3) is applicable to geometries containing edges and points. Several numerical examples are provided to demonstrate the efficiency and accuracy of the aforementioned algorithm in various geometries.

KW - Body of revolution

KW - Dielectric media

KW - Electromagnetics

KW - Fast Fourier transform

KW - Müller's integral equation

KW - Penetrable media

UR - http://www.scopus.com/inward/record.url?scp=85064327913&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064327913&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2019.04.005

DO - 10.1016/j.jcp.2019.04.005

M3 - Article

AN - SCOPUS:85064327913

VL - 390

SP - 152

EP - 174

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -