A semi-Lagrangian numerical method for geometric optics type problems

DOI10.1007/s10543-006-0081-0zbMath1105.65117OpenAlexW2052049607MaRDI QIDQ857546

Jean-David Benamou

Publication date: 19 December 2006

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-006-0081-0

zbMATH Keywords

algorithmHamilton-Jacobi equationnumerical examplesHamiltonian systemseikonal equation

Mathematics Subject Classification ID

Hamilton's equations (70H05) First-order nonlinear hyperbolic equations (35L60) Hamilton-Jacobi equations in mechanics (70H20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Geometric optics (78A05)

Cites Work

• Unnamed Item
• A geometrical optics-based numerical method for high frequency electromagnetic fields computations near fold caustics. I
• An introduction to Eulerian geometrical optics (1992--2002)
• A geometric optics method for high-frequency electromagnetic fields computations near fold caustics. II: The energy
• The theory of Legendrian unfoldings and first-order differential equations
• Computational high frequency wave propagation
• Direct computation of multivalued phase space solutions for Hamilton-Jacobi equations
• Oscillatory integrals, lagrange immersions and unfolding of singularities

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