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
(2007),
pp. 711740, ISSN 15403459 [doi]
(last updated on 2018/03/18)
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.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

