Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published March 2011 | Published + Submitted
Journal Article Open

Space-time FLAVORS: finite difference, multisymlectic, and pseudospectral integrators for multiscale PDEs

Abstract

We present a new class of integrators for stiff PDEs. These integrators are generalizations of FLow AVeraging integratORS (FLAVORS) for stiff ODEs and SDEs introduced in [32] with the following properties: (i) Multiscale: they are based on flow averaging and have a computational cost determined by mesoscopic steps in space and time instead of microscopic steps in space and time; (ii) Versatile: the method is based on averaging the flows of the given PDEs (which may have hidden slow and fast processes). This bypasses the need for identifying explicitly (or numerically) the slow variables or reduced effective PDEs; (iii) Nonintrusive: A pre-existing numerical scheme resolving the microscopic time scale can be used as a black box and easily turned into one of the integrators in this paper by turning the large coefficients on over a microscopic timescale and off during a mesoscopic timescale; (iv) Convergent over two scales: strongly over slow processes and in the sense of measures over fast ones; (v) Structure-preserving: for stiff Hamiltonian PDEs (possibly on manifolds), they can be made to be multi-symplectic, symmetry-preserving (symmetries are group actions that leave the system invariant) in all variables and variational.

Additional Information

© 2011 International Press. This work is supported by NSF grant CMMI-092600. We thank Guo Luo for stimulating discussions and Sydney Garstang for proofreading the manuscript.

Attached Files

Published - Tao2011p13681Dynam_Part_Differ_Eq.pdf

Submitted - 1104.0272.pdf

Files

Tao2011p13681Dynam_Part_Differ_Eq.pdf
Files (21.0 MB)
Name Size Download all
md5:6c3c7c105f5124329f48008d66339b61
16.1 MB Preview Download
md5:0b321b388e87ede00e507b8089b71f85
4.9 MB Preview Download

Additional details

Created:
August 22, 2023
Modified:
October 23, 2023