## Abstract

An algorithm based on the recursive operator algorithm is proposed to solve for the scattered field from an arbitrarily shaped, inhomogeneous scatterer. In this method, the scattering problem is first converted to an N‐scatterer problem. Then, an add‐on procedure is developed to obtain recursively an (n + 1)‐scatterer solution from an n‐scatterer solution by introducing an aggregate τ matrix in the recursive scheme. The nth aggregate τ_{n} matrix introduced is equivalent to a global τ matrix for n scatterers so that in the next recursion, only the two‐scatterer problem needs to be solved: One scatterer is the sum of the previous n scatterers, characterized by an nth aggregate τ_{n} matrix; the other is the (n + 1)th isolated scatterer, characterized by τ_{n + 1(1)}. If M is the number of harmonics used in the isolated scatterer T matrix and P is the number of harmonics used in the translation formulas, the computational effort at each recursion will be proportional to P^{2}M. (Here we assume M is less than P.) Consequently, the total computational effort to obtain the N‐scatterer aggregate τ_{N} matrix will be proportional to P^{2}MN. In the low‐frequency limit, the algorithm is linear in N because P, the number of the harmonics in the translation formulas, is independent of the size of the object.

Original language | English (US) |
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Pages (from-to) | 164-169 |

Number of pages | 6 |

Journal | Microwave and Optical Technology Letters |

Volume | 3 |

Issue number | 5 |

DOIs | |

State | Published - May 1990 |

Externally published | Yes |

## Keywords

- Scattering
- inhomogeneous scatterer
- numerical method

## ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics
- Electrical and Electronic Engineering