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, 11 (2). 566-585. ISSN 1540-3459
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(Document in English)
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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 |
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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) |
Statistics: | download |
Deposited On: | 16 Mar 2015 07:50 |
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