Substantial modifications of both the choice of the grids, the combination coefficients, the parallel data structures and the algorithms used for the combination technique lead to numerical methods which are scalable. This is demonstrated by the provision of error and complexity bounds and in performance studies based on a state of the art code for the solution of the gyrokinetic equations of plasma physics. The key ideas for a new fault-tolerant combination technique are mentioned. New algorithms for both initial- and eigenvalue problems have been developed and are shown to have good performance.