Math @ Duke

Publications [#287177] of Ingrid Daubechies
Papers Published
 Daubechies, I; Runborg, O; Zou, J, A Sparse Spectral Method for Homogenization Multiscale Problems,
Multiscale Modeling & Simulation, vol. 6 no. 3
(January, 2007),
pp. 711740, Society for Industrial & Applied Mathematics (SIAM), ISSN 15403459 [doi]
(last updated on 2019/05/19)
Abstract: We develop a new sparse spectral method, in which the fast Fourier transform (FFT) is replaced by RAℓSFA (randomized algorithm of sparse Fourier analysis); this is a sublinear randomized algorithm that takes time O(B log N) to recover a Bterm Fourier representation for a signal of length N, where we assume B ≪ N. To illustrate its potential, we consider the parabolic homogenization problem with a characteristic fine scale size ε. For fixed tolerance the sparse method has a computational cost of O( logε ) per time step, whereas standard methods cost at least O(ε1). We present a theoretical analysis as well as numerical results; they show the advantage of the new method in speed over the traditional spectral methods when ε is very small. We also show some ways to extend the methods to hyperbolic and elliptic problems. © 2007 Society for Industrial and Applied Mathematics.


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