Using K-branch entropy solutions for multivalued geometric Optics computations

Journal of Computational Physics

Volumn 180, Issue 1, 2002, Pages 155-182

  Gosse, Laurent ^a  

^a Istituto per le Applicazioni del Calcolo   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ENTROPY; NONLINEAR EQUATIONS;

COMPUTATIONAL TESTS; CONSERVATION LAW; EIKONAL EQUATION; ENTROPY SOLUTION; EXISTENCE AND UNIQUENESS RESULTS; GEOMETRIC OPTICS; MULTI-VALUED; MULTIBRANCH; SUPERIMPOSED SIGNAL; WKB SYSTEM;

GEOMETRICAL OPTICS;

EID: 0037143007     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2002.7085     Document Type: Article

References (59)

1. Global BV entropy solutions and uniqueness for hyperbolic systems of balance laws
2. Big ray tracing: Multivalued travel time field computation using viscosity solutions of the eikonal equation
3. Direct computation of multivalued phase space solutions for Hamilton-Jacobi equations
4. Geometrical optics and viscosity solutions
5. Construction of BGK models with a family of kinetic entropies for a given system of conservation laws
6. One-dimensional transport equations with discontinuous coefficients
7. Averaged multivalued solutions for scalar conservation laws
8. A kinetic formulation for multibranch entropy solutions of scalar conservation laws
9. Relaxation limits for a class of balance laws with kinetic formulation
10. The discrete one-sided Lipschits condition for convex scalar conservation laws
11. Hyperbolic Systems of Conservation Laws: The One-Dimensional Cauchy Problem
12. Decay of positive waves in nonlinear systems of conservation laws
13. Oleǐnik type estimates and uniqueness for n × n conservation laws
14. ∞ solutions of Temple class systems
15. Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems
16. The nonlinear Schroedinger equation as both a PDE and a dynamical system
17. Semi-classical Schrödinger equation with harmonic potential and non-linear perturbation
18. Viscosity solutions of Hamilton-Jacobi equations
19. On a class of nonstrictly hyperbolic and nonconservative systems
20. Multiphase computations in geometrical optics
21. High frequency wave propagation by the segment projection method
22. Numerical solution of the high frequency asymptotic expansion for the scalar wave equation
23. Finite Difference Methods for Geometrical Optics and Related Non-linear PDEs Approximating the High Frequency Helmholts Equation
24. Nonsoliton pulse evolution in normally dispersive fibers
25. Solutions in the large for nonlinear hyperbolic systems of equations
26. Decay of positive waves for n × n hyperbolic systems of balance laws
27. A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms
28. A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms
29. Numerical approximations of one-dimensional linear conservation equations
30. The viscosity-duality solutions approach to geometric optics for the Helmholtz equation
31. Convergence results for an inhomogeneous system arising in various high frequency approximations
32. Geometric singularities for solutions of single conservation laws
33. The behavior of solutions of the NLS equation in the semiclassical limit
34. Multi-phase computations of the semiclassical limit of the Schrödinger equation and related problems: Whitham vs. Wigner
35. Computation of high frequency fields near caustics
36. Geometrical theory of diffraction
37. The Cauchy problem in the large for nonlinear equations and for certain quasilinear systems of the first order in several space variables
38. Moment closure hierarchies for kinetic theories
39. A kinetic formulation of multidimensional scalar conservation laws and related equations
40. Kinetic formulation of the isentropic gas dynamics and p-systems
41. Admissible solutions of hyperbolic conservation laws
42. Uniform expansions at a caustic
43. Non oscillatory central differencing for hyperbolic conservation laws
44. Discontinuous solutions of nonlinear differential equations
45. Measure solutions to the linear multi-dimensional transport equation with non-smooth coefficients
46. Hyperbolic equations and frequency interactions
47. Some new results in multiphase geometrical optics
48. A fixed grid method for capturing the motion of self-interacting interfaces and related PDEs
49. Systèmes de Lois de Conservation
50. Multivalued geometrical optics: Wigner functions vs. WKB methods
51. A slowness matching finite difference method for traveltimes beyond transmission caustics
52. On the mathematical theory of fluid dynamic limits to conservation laws
53. Kinetic semi-discretization of scalar conservation laws and convergence by using averaging lemmas
54. Convergence of a semi-discrete kinetic scheme for the system of isentropic gas dynamics with γ = 3
55. Time regularity for the system of isentropic gas dynamics with γ = 3