A sparse spectral method for homogenization multiscale problems

Journal Article (Journal Article)

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 B-term 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(ε-1). 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.

Full Text

Duke Authors

Cited Authors

  • Daubechies, I; Runborg, O; Zou, J

Published Date

  • August 1, 2007

Published In

Volume / Issue

  • 6 / 3

Start / End Page

  • 711 - 740

Electronic International Standard Serial Number (EISSN)

  • 1540-3467

International Standard Serial Number (ISSN)

  • 1540-3459

Digital Object Identifier (DOI)

  • 10.1137/060676258

Citation Source

  • Scopus