TY - JOUR

T1 - Newton-Krylov solvers for the equation-free computation of coarse traveling waves

AU - Samaey, Giovanni

AU - Vanroose, Wim

AU - Roose, Dirk

AU - Kevrekidis, Ioannis G.

N1 - Funding Information:
The authors thank Pieter Van Leemput, Christophe Vandekerckhove, Kurt Lust and Tim Boonen for interesting discussions about various aspects of this work. Pieter Van Leemput provided us with Fig. 2 . G.S. is a Postdoctoral Fellow of the Fund for Scientific Research – Flanders. W.V. is supported by the Belgian Science Policy Office through its action “return grants”. This work was supported by the Fund for Scientific Research – Flanders through Research Project G.0130.03 (G.S., D.R., W.V.) and by the Interuniversity Attraction Poles Programme of the Belgian Science Policy Office through grant IUAP/V/22. The scientific responsibility rests with its authors. The research of I.G.K. was partially supported by the US DOE and DARPA.

PY - 2008/8/1

Y1 - 2008/8/1

N2 - For many complex dynamical systems, a separation of scales prevails between the (fine-scale) level of description of the available model, and the (coarse) level at which one would like to observe and analyze the system. For this type of problems, an "equation-free" framework has recently been proposed. Using appropriately initialized fine-scale simulations, one can build a coarse time-stepper to approximate a time-stepper for the unavailable coarse model. Here, we use this coarse time-stepper to estimate matrix-vector products in a Jacobian-free Newton-GMRES method. The GMRES convergence is accelerated with a preconditioner that is derived from an approximate coarse equation. We examine the numerical properties of the approach with the computation of coarse traveling wave solutions of two lattice Boltzmann models for planar streamer fronts.

AB - For many complex dynamical systems, a separation of scales prevails between the (fine-scale) level of description of the available model, and the (coarse) level at which one would like to observe and analyze the system. For this type of problems, an "equation-free" framework has recently been proposed. Using appropriately initialized fine-scale simulations, one can build a coarse time-stepper to approximate a time-stepper for the unavailable coarse model. Here, we use this coarse time-stepper to estimate matrix-vector products in a Jacobian-free Newton-GMRES method. The GMRES convergence is accelerated with a preconditioner that is derived from an approximate coarse equation. We examine the numerical properties of the approach with the computation of coarse traveling wave solutions of two lattice Boltzmann models for planar streamer fronts.

KW - Equation-free methods

KW - Model-based preconditioning

KW - Multiscale computation

KW - Newton-Krylov

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U2 - 10.1016/j.cma.2007.11.033

DO - 10.1016/j.cma.2007.11.033

M3 - Article

AN - SCOPUS:48849092313

SN - 0045-7825

VL - 197

SP - 3480

EP - 3491

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 43-44

ER -