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Eulerian Approximate Ray Tracing and Applications to Grid Generation

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

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  • Patrizia Bagnerini

    (Université de Nice, Laboratoire de Mathématiques CNRS n. 6621)

Abstract

We introduce a scheme to compute the viscosity solution of the Riemannian Eikonal equation, on a regular grid or triangular mesh and which uses the order given by the Sweeping algorithm, to update the points. We also compute the bicharacteristic curves of the viscosity solution in a domain Ω in Eulerian way: instead of solving a system of ODE for every source point belongs to ∂Ω, we label each ray by a parameter θ and thus we compute a function θ = θ(s, t), θ: Ω ⊂ℝ2 → ℝ2, whose level sets are the rays. We then present some numerical results.

Suggested Citation

  • Patrizia Bagnerini, 2003. "Eulerian Approximate Ray Tracing and Applications to Grid Generation," Springer Books, in: Thomas Y. Hou & Eitan Tadmor (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 335-346, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55711-8_30
    DOI: 10.1007/978-3-642-55711-8_30
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