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Multiscale discrete approximations of Fourier integral operators associated with canonical transformations and caustics

Van De Hoop, Maarten and Uhlmann, Gunther and Vasy, Andras and Wendt, Herwig Multiscale discrete approximations of Fourier integral operators associated with canonical transformations and caustics. (2013) Multiscale Modeling and Simulation, vol. 11 (n° 2). pp. 566-585. ISSN 1540-3459

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Official URL: http://dx.doi.org/10.1137/120889642

Abstract

We develop an algorithm for the computation of general Fourier integral operators associated with canonical graphs. The algorithm is based on dyadic parabolic decomposition using wave packets and enables the discrete approximate evaluation of the action of such operators on data in the presence of caustics. The procedure consists of constructing a universal operator representation through the introduction of locally singularity-resolving diffeomorphisms, thus enabling the application of wave packet--driven computation, and of constructing the associated pseudodifferential joint-partition of unity on the canonical graphs. We apply the method to a parametrix of the wave equation in the vicinity of a cusp singularity.

Item Type:Article
Additional Information:Thanks to SIAM editor. The definitive version is available at http://epubs.siam.org/doi/abs/10.1137/120889642
HAL Id:hal-01131774
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Other partners > Purdue University (USA)
Other partners > University of California - UCIrvine (USA)
Other partners > Stanford University (USA)
Other partners > University of Washington (USA)
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Deposited By: IRIT IRIT
Deposited On:16 Mar 2015 07:50

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