Paper Info
Title
Fast wave computation via Fourier integral operators.
Abstract
This paper presents a numerical method for "time upscaling" wave equations, i.e., performing time steps not limited by the Courant-Friedrichs-Lewy (CFL) condition. The proposed method leverages recent work on fast algorithms for pseudodifferential and Fourier integral operators (FIO). This algorithmic approach is not asymptotic: it is shown how to construct an exact FIO propagator by 1) solving Hamilton-Jacobi equations for the phases, and 2) sampling rows and columns of low-rank matrices at random for the amplitudes. The setting of interest is that of scalar waves in two-dimensional smooth periodic media (of class C-infinity over the torus), where the bandlimit N of the waves goes to infinity. In this setting, it is demonstrated that the algorithmic complexity for solving the wave equation to fixed time T similar or equal to 1. call be as low as O(N-2 log N) with controlled accuracy. Numerical experiments show that the time complexity can be lower than that of a spectral method in certain situations of physical interest.
Year
DOI
Venue
2012
10.1090/S0025-5718-2012-02557-9
MATHEMATICS OF COMPUTATION
Keywords
DocType
Volume
Wave equations,Fourier integral operators,discrete symbol calculus,random sampling,separated approximation,multiscale computations
Journal
81
Issue
ISSN
Citations 
279
0025-5718
3
PageRank 
References 
Authors
0.44
14
2
Name
Order
Citations
PageRank
Laurent Demanet175057.81
Lexing Ying21273103.92