An energy conservative \(hp\)-method for Liouville's equation of geometrical optics

DOI10.1007/s10915-021-01612-xzbMath1496.65187OpenAlexW3201363517WikidataQ114225590 ScholiaQ114225590MaRDI QIDQ1983181

R. A. M. van Gestel, M. J. H. Anthonissen, Wilbert L. Ijzerman, Jan H. M. ten Thije Boonkkamp

Publication date: 15 September 2021

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-021-01612-x

zbMATH Keywords

phase spaceenergy conservationgeometrical opticsdiscontinuous GalerkinLiouville's equation

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Hyperbolic conservation laws (35L65) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Geometric optics (78A05) Spectral, collocation and related methods applied to problems in optics and electromagnetic theory (78M22)

Related Items (2)

A hybrid semi-Lagrangian DG and ADER-DG solver on a moving mesh for Liouville's equation of geometrical optics ⋮ An ADER discontinuous Galerkin method on moving meshes for Liouville's equation of geometrical optics

Cites Work

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• CFL conditions for Runge-Kutta discontinuous Galerkin methods on triangular grids
• Geometry effects in nodal discontinuous Galerkin methods on curved elements that are provably stable
• Runge-Kutta methods with minimum storage implementations
• Low-storage Runge-Kutta schemes
• Runge-Kutta methods for linear ordinary differential equations
• A conservative staggered-grid Chebyshev multidomain method for compressible flows. II: A semi-structured method
• Noncorming matching conditions for coupling spectral and finite element methods
• A robust CFL condition for the discontinuous Galerkin method on triangular meshes
• A novel scheme for Liouville's equation with a discontinuous Hamiltonian and applications to geometrical optics
• Analysis of an $hp$-Nonconforming Discontinuous Galerkin Spectral Element Method for Wave Propagation
• Implementing Spectral Methods for Partial Differential Equations
• Computation of electromagnetic scattering with a non‐conforming discontinuous spectral element method
• Weight-Adjusted Discontinuous Galerkin Methods: Curvilinear Meshes
• Introduction to Quasi-Monte Carlo Integration and Applications

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