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Center for Scientific Computation and Mathematical Modeling

Research Activities > Programs > High Frequency Wave Propagation 2005 > Emmanuel Candes

High Frequency Wave Propagation

CSIC Building (#406), Seminar Room 4122.
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The Phase Flow Method


Emmanuel Candes

Applied and Computational Mathematics at California Institute of Technology

Abstract:   This talk introduces the phase flow method (PFM), 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 time using standard ODE integrators and builds the phase map for large time with the help of a local interpolation scheme together with the group property of the phase flow. The computational complexity of building the whole phase map is usually that of tracing a few rays. In addition, the PFM is very accurate. Once the phase map is available, integrating the ODE for initial conditions on the invariant manifold only utilizes local interpolation, thus having constant complexity. We present applications in the field of high frequency wave propagation, and show how to use the PFM to 1) rapidly construct wavefronts, 2) calculate the wave amplitude along these wavefronts and 3) rapidly evaluate multiple wave arrival times at arbitrary locations.