Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Uniformly high-order accurate nonoscillatory schemes
SIAM Journal on Numerical Analysis
Fast wavelet based algorithms for linear evolution equations
SIAM Journal on Scientific Computing
Numerical solution of the high frequency asymptotic expansion for the scalar wave equation
Journal of Computational Physics
Journal of Computational Physics
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
A new Eulerian method for the computation of propagating short acoustic and electromagnetic pulses
Journal of Computational Physics
A fixed grid method for capturing the motion of self-intersecting wavefronts and related PDEs
Journal of Computational Physics
High-frequency wave propagation by the segment projection method
Journal of Computational Physics
Geometric optics in a phase-space-based level set and Eulerian framework
Journal of Computational Physics
An Introduction to Eulerian Geometrical Optics (1992–2002)
Journal of Scientific Computing
A Slowness Matching Eulerian Method for Multivalued Solutions of Eikonal Equations
Journal of Scientific Computing
Short note: Fast geodesics computation with the phase flow method
Journal of Computational Physics
High order numerical methods to a type of delta function integrals
Journal of Computational Physics
Parallel algorithms for approximation of distance maps on parametric surfaces
ACM Transactions on Graphics (TOG)
The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation
Journal of Computational Physics
A Hybrid Phase Flow Method for Solving the Liouville Equation in a Bounded Domain
SIAM Journal on Numerical Analysis
Solving the stationary Liouville equation via a boundary element method
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
This paper introduces the phase flow method, a novel, accurate and fast approach for constructing phase maps for nonlinear autonomous ordinary differential equations. The method operates by initially constructing the phase map for small times using a standard ODE integration rule and builds up the phase map for larger times with the help of a local interpolation scheme together with the group property of the phase flow. The computational complexity of building up the complete phase map is usually that of tracing a few rays. In addition, the phase flow method is provably and empirically very accurate. Once the phase map is available, integrating the ODE for initial conditions on the invariant manifold only makes use of local interpolation, thus having constant complexity. The paper develops applications in the field of high frequency wave propagation, and shows how to use the phase flow method to (1) rapidly propagate wave fronts, (2) rapidly calculate wave amplitudes along these wave fronts, and (3) rapidly evaluate multiple wave arrival times at arbitrary locations.