  For many complex dynamical systems, a separation of scales prevails between
the (microscopic) level of description of the available model, and the
(macroscopic) 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 microscopic simulations, one can
build a coarse-grained time-stepper to approximate a time-stepper for the
unavailable macroscopic model. Here, we show how one can use this
coarse-grained time-stepper to compute coarse-grained traveling wave solutions
of a lattice Boltzmann model. In a moving frame, emulated by performing a
shift-back operation after the coarse-grained time-step, the traveling wave
appears as a steady state, which is computed using an iterative method, such as
Newton--GMRES. To accelerate convergence of the GMRES procedure, a macroscopic
model-based preconditioner is used, which is derived from the lattice Boltzmann
model using a Chapman--Enskog expansion. We illustrate the approach on a
lattice Boltzmann model for the Fisher equation and on a model for ionization
waves.
