Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources

Mikhail A. Bochev (Corresponding Author), A. M. Hanse, Ravitej Uppu

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)

Abstract

Light incident on a layer of scattering material such as a piece of sugar or white paper forms a characteristic speckle pattern in transmission and reflection. The information hidden in the correlations of the speckle pattern with varying frequency, polarization and angle of the incident light can be exploited for applications such as biomedical imaging and high-resolution microscopy. Conventional computational models for multi-frequency optical response involve multiple solution runs of Maxwell’s equations with monochromatic sources. Exponential Krylov subspace time solvers are promising candidates for improving efficiency of such models, as single monochromatic solution can be reused for the other frequencies without performing full time-domain computations at each frequency. However, we show that the straightforward implementation appears to have serious limitations. We further propose alternative ways for efficient solution through Krylov subspace methods. Our methods are based on two different splittings of the unknown solution into different parts, each of which can be computed efficiently. Experiments demonstrate a significant gain in computation time with respect to the standard solvers.
Original languageEnglish
Pages (from-to)474-485
Number of pages12
JournalJournal of computational and applied mathematics
Volume340
DOIs
Publication statusPublished - 1 Oct 2018

Fingerprint

Time Integration
Speckle
Modeling
Maxwell equations
Biomedical Imaging
Sugars
Krylov Subspace Methods
Krylov Subspace
Microscopic examination
Multiple Solutions
Efficient Solution
Maxwell's equations
Microscopy
Scattering
Computational Model
Polarization
Imaging techniques
Time Domain
High Resolution
Angle

Cite this

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title = "Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources",
abstract = "Light incident on a layer of scattering material such as a piece of sugar or white paper forms a characteristic speckle pattern in transmission and reflection. The information hidden in the correlations of the speckle pattern with varying frequency, polarization and angle of the incident light can be exploited for applications such as biomedical imaging and high-resolution microscopy. Conventional computational models for multi-frequency optical response involve multiple solution runs of Maxwell’s equations with monochromatic sources. Exponential Krylov subspace time solvers are promising candidates for improving efficiency of such models, as single monochromatic solution can be reused for the other frequencies without performing full time-domain computations at each frequency. However, we show that the straightforward implementation appears to have serious limitations. We further propose alternative ways for efficient solution through Krylov subspace methods. Our methods are based on two different splittings of the unknown solution into different parts, each of which can be computed efficiently. Experiments demonstrate a significant gain in computation time with respect to the standard solvers.",
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Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources. / Bochev, Mikhail A. (Corresponding Author); Hanse, A. M.; Uppu, Ravitej .

In: Journal of computational and applied mathematics, Vol. 340, 01.10.2018, p. 474-485.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Exponential Krylov time integration for modeling multi-frequency optical response with monochromatic sources

AU - Bochev, Mikhail A.

AU - Hanse, A. M.

AU - Uppu, Ravitej

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AB - Light incident on a layer of scattering material such as a piece of sugar or white paper forms a characteristic speckle pattern in transmission and reflection. The information hidden in the correlations of the speckle pattern with varying frequency, polarization and angle of the incident light can be exploited for applications such as biomedical imaging and high-resolution microscopy. Conventional computational models for multi-frequency optical response involve multiple solution runs of Maxwell’s equations with monochromatic sources. Exponential Krylov subspace time solvers are promising candidates for improving efficiency of such models, as single monochromatic solution can be reused for the other frequencies without performing full time-domain computations at each frequency. However, we show that the straightforward implementation appears to have serious limitations. We further propose alternative ways for efficient solution through Krylov subspace methods. Our methods are based on two different splittings of the unknown solution into different parts, each of which can be computed efficiently. Experiments demonstrate a significant gain in computation time with respect to the standard solvers.

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