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Fully Discrete Energy Stable Methods for Maxwell's Equations in Nonlinear Media Li, Fengyan
Description
The propagation of electromagnetic waves is modeled by time-dependent Maxwell's equations coupled with constitutive laws that describe the response of the media. In this work, we examine a nonlinear optical model that describes electromagnetic waves in linear Lorentz and nonlinear Kerr and Raman media. To design efficient, accurate, and stable computational methods, we apply high order discontinuous Galerkin discretizations and finite difference schemes in space. The challenge to achieve provable stability for fully-discrete methods lies in the temporal discretizations of the nonlinear terms. To overcome this, novel modification is proposed for the second-order leap-frog and implicit trapezoidal time integrators. The performance of the method is demonstrated via numerical examples.
Item Metadata
Title |
Fully Discrete Energy Stable Methods for Maxwell's Equations in Nonlinear Media
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2019-05-15T10:45
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Description |
The propagation of electromagnetic waves is modeled by
time-dependent Maxwell's equations coupled with constitutive laws that
describe the response of the media. In this work, we examine a nonlinear
optical model that describes electromagnetic waves in linear Lorentz and
nonlinear Kerr and Raman media. To design efficient, accurate, and
stable computational methods, we apply high order discontinuous Galerkin
discretizations and finite difference schemes in space. The challenge
to achieve provable stability for fully-discrete methods lies in the
temporal discretizations of the nonlinear terms. To overcome this, novel
modification is proposed for the second-order leap-frog and implicit
trapezoidal time integrators. The performance of the method is
demonstrated via numerical examples.
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Extent |
26.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Rensselaer Polytechnic Institute
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Series | |
Date Available |
2019-11-12
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0385165
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International