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

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

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Article number108881
Pages (from-to)1-33
Number of pages33
JournalJournal of Computational Physics
Volume398
DOIs
Publication statusPublished - 1 Dec 2019

Keywords

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

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