  A new method for solving numerically stochastic partial differential
equations (SPDEs) with multiple scales is presented. The method combines a
spectral method with the heterogeneous multiscale method (HMM) presented in [W.
E, D. Liu, and E. Vanden-Eijnden, Comm. Pure Appl. Math., 58(11):1544--1585,
2005]. The class of problems that we consider are SPDEs with quadratic
nonlinearities that were studied in [D. Blomker, M. Hairer, and G.A. Pavliotis,
Nonlinearity, 20(7):1721--1744, 2007.] For such SPDEs an amplitude equation
which describes the effective dynamics at long time scales can be rigorously
derived for both advective and diffusive time scales. Our method, based on
micro and macro solvers, allows to capture numerically the amplitude equation
accurately at a cost independent of the small scales in the problem. Numerical
experiments illustrate the behavior of the proposed method.
