Tao, Molei and Owhadi, Houman and Marsden, Jerrold E. (2011) Space-time FLAVORS: finite difference, multisymlectic, and pseudospectral integrators for multiscale PDEs. Dynamics of Partial Differential Equations, 8 (1). pp. 21-45. ISSN 1548-159X http://resolver.caltech.edu/CaltechAUTHORS:20110502-134102771
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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  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.|
|Subject Keywords:||Stiff PDEs; FLow AVeraging integratORS|
|Classification Code:||1991 Mathematics Subject Classification: 35, 65.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||03 May 2011 16:51|
|Last Modified:||26 Dec 2012 13:12|
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