### Abstract

Existing approaches to the solution of the inverse scattering problems in two and three dimensions rely on linearization of the Helmholtz equation, which requires the knowledge of the Fréchet derivative of the far field with respect to the index of refraction. We present an efficient algorithm for this perturbational calculation in two dimensions. Our method is based on the merging and splitting procedures already established for the solution of the Lippmann-Schwinger equation [2], [3], [4]. For an m-by-m wavelength problem, the algorithm obtains perturbations to scattered waves for m distinct incident waves in O(m ^{3}) steps.

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

Pages (from-to) | 627-636 |

Number of pages | 10 |

Journal | Discrete and Continuous Dynamical Systems |

Volume | 18 |

Issue number | 4 |

State | Published - Aug 2007 |

### Fingerprint

### Keywords

- Fast direct algorithms
- Merging formulae
- Scattering matrix

### ASJC Scopus subject areas

- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Analysis

### Cite this

*Discrete and Continuous Dynamical Systems*,

*18*(4), 627-636.

**Rapid perturbational calculations for the helmholtz equation in two dimensions.** / Shim, Sang Yeun; Capistran, Marcos; Chen, Yu.

Research output: Contribution to journal › Article

*Discrete and Continuous Dynamical Systems*, vol. 18, no. 4, pp. 627-636.

}

TY - JOUR

T1 - Rapid perturbational calculations for the helmholtz equation in two dimensions

AU - Shim, Sang Yeun

AU - Capistran, Marcos

AU - Chen, Yu

PY - 2007/8

Y1 - 2007/8

N2 - Existing approaches to the solution of the inverse scattering problems in two and three dimensions rely on linearization of the Helmholtz equation, which requires the knowledge of the Fréchet derivative of the far field with respect to the index of refraction. We present an efficient algorithm for this perturbational calculation in two dimensions. Our method is based on the merging and splitting procedures already established for the solution of the Lippmann-Schwinger equation [2], [3], [4]. For an m-by-m wavelength problem, the algorithm obtains perturbations to scattered waves for m distinct incident waves in O(m 3) steps.

AB - Existing approaches to the solution of the inverse scattering problems in two and three dimensions rely on linearization of the Helmholtz equation, which requires the knowledge of the Fréchet derivative of the far field with respect to the index of refraction. We present an efficient algorithm for this perturbational calculation in two dimensions. Our method is based on the merging and splitting procedures already established for the solution of the Lippmann-Schwinger equation [2], [3], [4]. For an m-by-m wavelength problem, the algorithm obtains perturbations to scattered waves for m distinct incident waves in O(m 3) steps.

KW - Fast direct algorithms

KW - Merging formulae

KW - Scattering matrix

UR - http://www.scopus.com/inward/record.url?scp=35248836500&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35248836500&partnerID=8YFLogxK

M3 - Article

VL - 18

SP - 627

EP - 636

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 4

ER -