Fast-phase space computation of multiple arrivals

DOI10.1073/pnas.102476599zbMath1002.65113OpenAlexW2029299802WikidataQ34063532 ScholiaQ34063532MaRDI QIDQ4547714

S. B. Fomel, James A. Sethian

Publication date: 11 September 2002

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: http://www.pnas.org/content/vol99/issue11/#APPLIED_MATHEMATICS

zbMATH Keywords

eikonal equationstatic Hamilton-Jacobi equationscharacteristic equationssemi-Lagrangian methodsordered upwind methodsDijkstra-like methodsphase-space solution

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Finite difference methods for boundary value problems involving PDEs (65N06) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25) Boundary value problems for nonlinear first-order PDEs (35F30)

Related Items

Hamilton-Green solver for the forward and adjoint problems in photoacoustic tomography, A field-space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations, Fast geodesics computation with the phase flow method, The phase flow method, TWO MOMENT SYSTEMS FOR COMPUTING MULTIPHASE SEMICLASSICAL LIMITS OF THE SCHRÖDINGER EQUATION, A level set based Eulerian method for paraxial multivalued traveltimes, Computing multi-valued velocity and electric fields for 1D Euler-Poisson equations, A geometrical optics-based numerical method for high frequency electromagnetic fields computations near fold caustics. I, Analysis of a fast method for solving the high frequency Helmholtz equation in one dimension, Computation of transmissions and reflections in geometrical optics via the reduced Liouville equation, HYPERBOLIC DOMAINS OF DETERMINACY AND HAMILTON–JACOBI EQUATIONS, Computational high frequency waves through curved interfaces via the Liouville equation and geometric theory of diffraction, On the Last Geometric Statement of Jacobi, Geometric optics in a phase-space-based level set and Eulerian framework, Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with discontinuous local wave speeds, Ordered line integral methods for solving the eikonal equation, A boundary integral method for modelling vibroacoustic energy distributions in uncertain built up structures, Mathematical and computational methods for semiclassical Schrödinger equations, CAPTURING MULTI-VALUED SOLUTIONS OF SHALLOW WATER EQUATION BY LEVEL SET METHOD, Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems

Cites Work

• A fixed grid method for capturing the motion of self-intersecting wavefronts and related PDEs
• Big ray tracing: Multivalued travel time field computation using viscosity solutions of the eikonal equation
• A new Eulerian method for the computation of propagating short acoustic and electromagnetic pulses.
• Fast Marching Methods
• Optimal prediction and the Mori–Zwanzig representation of irreversible processes
• Ordered upwind methods for static Hamilton–Jacobi equations
• Oscillatory integrals, lagrange immersions and unfolding of singularities
• Efficient algorithms for globally optimal trajectories
• A fast marching level set method for monotonically advancing fronts.