Geometric optics in a phase-space-based level set and Eulerian framework

Journal of Computational Physics

Volumn 179, Issue 2, 2002, Pages 622-648

  Osher, Stanley ^a   Cheng, Li Tien ^b   Kang, Myungjoo ^a   Shim, Hyeseon ^a   Tsai, Yen Hsi ^c  

^a Pacific Palisades   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GEOMETRICAL OPTICS; PARTIAL DIFFERENTIAL EQUATIONS; PHASE SPACE METHODS; REFRACTION; WAVE PROPAGATION;

BICHARACTERISTICS; EULERIAN FRAMEWORK; GEOMETRIC OPTICS; LEVEL SET APPROACH; LEVEL SET FRAMEWORK; MULTI-VALUED SOLUTION; PHASE SPACES; SPACE-BASED; SPATIAL SPACES; WAVE FRONT;

WAVEFRONTS;

EID: 0036647932     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2002.7080     Document Type: Article

References (45)

1. Big ray tracing and Eikonal solver on unstructured grids: Application to the computation of a multivalued travel-time field in the Marmousi model
2. Level set approach to mean curvature flow in arbitrary codimension
3. Singularities of Differential Maps
4. An Eulerian numerical method for geometric optics
5. Big ray tracing: Multi-valued travel time field computation using viscosity solutions of the Eikonal equation
6. Direct solution of multi-valued phase-space solutions for Hamilton-Jacobi equations
7. Markov chain approximations for deterministic control problems with Affine dynamics and quadratic cost in the control
8. A kinetic formulation for multi-branch entropy solutions of scalar conservation laws
9. Motion of curves in three spatial dimensions using a level set approach
10. A simple level set method for solving Stefan problems
11. Euclidean distance mapping
12. Oscillatory integrals, Lagrange immersions and unfolding of singularities
13. Numerical resolution of the high frequency asymptotic expansion of the scalar wave equation
14. Multi-Phase Computation in Geometrical Optics
15. High Frequency Wave Propagation by the Segment Projection Method
16. A new Eulerian method for the computation of propagating short acoustic and electromagnetic pulses
17. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
18. Fast Phase Space Computation of Multiple Arrivals
19. Barriers, Boundaries, Motion of Manifolds
20. Two new methods for simulating photolithography development in 3D
21. The theory of Legendrian unfoldings and first order differential equations
22. Weighted ENO schemes for Hamilton Jacobi equations
23. The Immersed Interface Method-A Numerical Approach to Partial Differential Equations with Interfaces
24. Marching cubes: A high resolution 3D surface reconstruction algorithm
25. Co-dimension 2 geodesic active contours for MRA segmentation
26. Level set methods: An overview and some recent results
27. Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations
28. A PDE-based fast local level set method
29. Fixed grid method for capturing the motion of self-intersecting interfaces and related PDEs
30. Transport equations for elastic and other waves in random media
31. Fast marching level set methods for three dimensional photolithography development
32. Efficient implementation of essentially nonoscillatory shock-capturing schemes
33. A new class of optimal high-order strong-stability-preserving time discretization methods
34. A level set method for computing solutions to incompressible two-phase flow
35. A Slowness Matching Finite Difference Method for Travel times beyond Transmission Caustics
36. Interface Tracking Methods with Applications to Multiphase Flow
37. Interface tracking in two-phase flows
38. Fast sweeping algorithms for a class of Hamilton-Jacobi equations
39. Efficient algorithms for globally optimal trajectories
40. Estimation of multivalued arrivals in 3D models using wavefront construction-Part I
41. Part II: Tracing and interpolation
42. Traveltime and amplitude estimation using wavefront construction
43. On the quantum correction for thermodynamic equilibrium
44. Implict and nonparametric shape reconstruction from unorganized points using variational level set method