@article{e710483aaf0d4ffea88863624cca6a69,
title = "A multi-scale Gaussian beam parametrix for the wave equation: The Dirichlet boundary value problem",
abstract = "We present a construction of a multi-scale Gaussian beam parametrix for the Dirichlet boundary value problem associated with the wave equation, and study its convergence rate to the true solution in the highly oscillatory regime. The construction elaborates on the wave-atom parametrix of Bao, Qian, Ying, and Zhang and extends to a multi-scale setting the technique of Gaussian beam propagation from a boundary of Katchalov, Kurylev and Lassas.",
keywords = "Boundary-value problem, Gaussian beam, Parametrix, Wave equation, Wave-atom, FIELDS, APPROXIMATION, FRAME, FOURIER INTEGRAL-OPERATORS, REGULARITY, WAVEPACKET TRANSFORMS, CONSTRUCTION, ATOMS, COMPUTATION",
author = "Michele Berra and {de Hoop}, {Maarten V.} and Romero, {Jos{\'e} Luis}",
note = "Funding Information: M.B. gratefully acknowledges support from the Fondazione CRT . M.V.d.H. gratefully acknowledges support from the Simons Foundation under the MATH + X program, the National Science Foundation under grant DMS-1559587 , and the corporate members of the Geo-Mathematical Group at Rice University. J.L.R. gratefully acknowledges support from the Austrian Science Fund (FWF): P 29462 - N35 and Y 1199 ; from a Marie Curie fellowship, within the 7th European Community Framework program , under grant PIIF-GA-2012-327063 ; and from the WWTF grant INSIGHT (MA16-053) . Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",
year = "2022",
month = feb,
day = "5",
doi = "10.1016/j.jde.2021.11.043",
language = "English",
volume = "309",
pages = "949--993",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "ACADEMIC PRESS INC ELSEVIER SCIENCE",
}