Abstract Details
Abstracts
Author: William J Barham
Requested Type: Poster
Submitted: 2024-04-12 15:56:00
Co-authors: Y. Güçlü, P. J. Morrison, E. Sonnendrücker
Contact Info:
The University of Texas at Austin
2515 Speedway
Austin, TX 78712
United States
Abstract Text:
Many asymptotic models describing the interaction of light and matter are characterized by a self-consistent (field dependent) nonlinear polarization and magnetization. For example, a model relevant in plasma physics is the ponderomotive force which, when considered self-consistently, induces a reciprocal density dependent index of refraction. Every model describing nonlinear constitutive relations for Maxwell's equations may be described by a single, elegant Hamiltonian formalism which accommodates arbitrary polarizations and magnetizations. Moreover, this modeling framework may be leveraged to design energy-stable and Gauss-conserving finite element methods to spatially discretize Maxwell's equations in nonlinear media. As this spatially discrete system is Hamiltonian, it may be integrated in time using the wealth of structure-preserving methods for Hamiltonian ODEs (e.g. symplectic or energy conserving methods). In particular, systems amenable to Hamiltonian splitting methods admit a particularly convenient time-integration scheme yielding a simple and efficient structure-preserving fully-discrete scheme. This method is applied to a model problem of cubicly nonlinear electromagnetic media to demonstrate its efficacy.
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