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

An efficient algorithm for a class of stochastic forward and inverse Maxwell models in \(\mathbb{R}^3\). (English) Zbl 1453.65017

J. Comput. Phys. 398, Article ID 108881, 33 p. (2019).
Summary: 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 \(\mathbb{R}^3\). 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.

Cited in 3 Documents

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
35R60 PDEs with randomness, stochastic partial differential equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
78A25 Electromagnetic theory (general)
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory

Keywords:

dielectric; surface integral equation; spectral approximations; generalized polynomial chaos; Bayesian inverse algorithm

Software:

BEM++; TMATROM
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Full Text: DOI

References:

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