### Abstract

We describe an efficient algorithm for reconstruction of the electromagnetic parameters of an unbounded dielectric medium from noisy cross section data induced by a point source in ℝ^{3}. The efficiency of our Bayesian inverse algorithm for the parameters is based on developing an offline high order forward stochastic model and also an associated deterministic dielectric media Maxwell solver. Underlying the inverse/offline approach is our high order fully discrete Galerkin algorithm for solving an equivalent surface integral equation reformulation that is stable for all frequencies. The efficient algorithm includes approximating the likelihood distribution in the Bayesian model by a decomposed fast generalized polynomial chaos (gPC) model as a surrogate for the forward model. Offline construction of the gPC model facilitates fast online evaluation of the posterior distribution of the dielectric medium parameters. Parallel computational experiments demonstrate the efficiency of our deterministic, forward stochastic, and inverse dielectric computer models.

Language | English |
---|---|

Article number | 108881 |

Pages | 1-33 |

Number of pages | 33 |

Journal | Journal of Computational Physics |

Volume | 398 |

DOIs | |

Publication status | Published - 1 Dec 2019 |

### Fingerprint

### Keywords

- Dielectric
- Surface integral equation
- Spectral approximations
- Generalized polynomial chaos
- Bayesian

### Cite this

^{3}.

*Journal of Computational Physics*,

*398*, 1-33. [108881]. https://doi.org/10.1016/j.jcp.2019.108881

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^{3}',

*Journal of Computational Physics*, vol. 398, 108881, pp. 1-33. https://doi.org/10.1016/j.jcp.2019.108881

**An efficient algorithm for a class of stochastic forward and inverse Maxwell models in ℝ ^{3}.** / Ganesh, M.; Hawkins, S. C.; Volkov, D.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - An efficient algorithm for a class of stochastic forward and inverse Maxwell models in ℝ3

AU - Ganesh, M.

AU - Hawkins, S. C.

AU - Volkov, D.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - We describe an efficient algorithm for reconstruction of the electromagnetic parameters of an unbounded dielectric medium from noisy cross section data induced by a point source in ℝ3. The efficiency of our Bayesian inverse algorithm for the parameters is based on developing an offline high order forward stochastic model and also an associated deterministic dielectric media Maxwell solver. Underlying the inverse/offline approach is our high order fully discrete Galerkin algorithm for solving an equivalent surface integral equation reformulation that is stable for all frequencies. The efficient algorithm includes approximating the likelihood distribution in the Bayesian model by a decomposed fast generalized polynomial chaos (gPC) model as a surrogate for the forward model. Offline construction of the gPC model facilitates fast online evaluation of the posterior distribution of the dielectric medium parameters. Parallel computational experiments demonstrate the efficiency of our deterministic, forward stochastic, and inverse dielectric computer models.

AB - We describe an efficient algorithm for reconstruction of the electromagnetic parameters of an unbounded dielectric medium from noisy cross section data induced by a point source in ℝ3. The efficiency of our Bayesian inverse algorithm for the parameters is based on developing an offline high order forward stochastic model and also an associated deterministic dielectric media Maxwell solver. Underlying the inverse/offline approach is our high order fully discrete Galerkin algorithm for solving an equivalent surface integral equation reformulation that is stable for all frequencies. The efficient algorithm includes approximating the likelihood distribution in the Bayesian model by a decomposed fast generalized polynomial chaos (gPC) model as a surrogate for the forward model. Offline construction of the gPC model facilitates fast online evaluation of the posterior distribution of the dielectric medium parameters. Parallel computational experiments demonstrate the efficiency of our deterministic, forward stochastic, and inverse dielectric computer models.

KW - Dielectric

KW - Surface integral equation

KW - Spectral approximations

KW - Generalized polynomial chaos

KW - Bayesian

UR - http://www.scopus.com/inward/record.url?scp=85070882792&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2019.108881

DO - 10.1016/j.jcp.2019.108881

M3 - Article

VL - 398

SP - 1

EP - 33

JO - Journal of Computational Physics

T2 - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

M1 - 108881

ER -

^{3}. Journal of Computational Physics. 2019 Dec 1;398:1-33. 108881. https://doi.org/10.1016/j.jcp.2019.108881