An Eulerian method for capturing caustics

DOI10.1006/jcph.2000.6530zbMath0958.65076OpenAlexW2042508339MaRDI QIDQ1577028

Ian Solliec, Jean-David Benamou

Publication date: 30 March 2001

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/inria-00072873/file/RR-3786.pdf

zbMATH Keywords

Hamilton-Jacobi equationviscosity solutionnumerical examplestransport equationEuler methodcausticsray tracing

Mathematics Subject Classification ID

Related Items (11)

Hamilton-Green solver for the forward and adjoint problems in photoacoustic tomography ⋮ A level set-based Eulerian approach for anisotropic wave propagation ⋮ A level set based Eulerian method for paraxial multivalued traveltimes ⋮ A geometrical optics-based numerical method for high frequency electromagnetic fields computations near fold caustics. I ⋮ Computation of transmissions and reflections in geometrical optics via the reduced Liouville equation ⋮ On the Last Geometric Statement of Jacobi ⋮ Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with discontinuous local wave speeds ⋮ Paraxial eikonal solvers for anisotropic quasi-P travel times. ⋮ Mathematical and computational methods for semiclassical Schrödinger equations ⋮ Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems ⋮ Jacobi’s last geometric statement extends to a wider class of Liouville surfaces

Cites Work

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• Big ray tracing: Multivalued travel time field computation using viscosity solutions of the eikonal equation
• Numerical solution of the high frequency asymptotic expansion for the scalar wave equation
• Two Approximations of Solutions of Hamilton-Jacobi Equations
• Viscosity Solutions of Hamilton-Jacobi Equations
• Direct computation of multivalued phase space solutions for Hamilton-Jacobi equations

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