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

M. Ganesh, S. C. Hawkins, D. Volkov

Research output: Contribution to journalArticleResearchpeer-review

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 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.

LanguageEnglish
Article number108881
Pages1-33
Number of pages33
JournalJournal of Computational Physics
Volume398
DOIs
Publication statusPublished - 1 Dec 2019

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Efficient Algorithms
Polynomial Chaos
Generalized Polynomials
Chaos theory
Higher Order
Surface integral
chaos
Polynomials
Computer Model
polynomials
Bayesian Model
Point Source
Reformulation
Posterior distribution
Computational Experiments
Galerkin
Model
Stochastic Model
Stochastic models
Likelihood

Keywords

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

Cite this

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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 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.",
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An efficient algorithm for a class of stochastic forward and inverse Maxwell models in ℝ3. / Ganesh, M.; Hawkins, S. C.; Volkov, D.

In: Journal of Computational Physics, Vol. 398, 108881, 01.12.2019, p. 1-33.

Research output: Contribution to journalArticleResearchpeer-review

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