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We introduce a high-performance simulation framework that permits thesemi-independent, task-based solution of sets of partial differentialequations, typically manifesting as updates to a collection of `patches' inspace-time. A hybrid MPI/OpenMP execution model is adopted, where work tasksare controlled by a rank-local `dispatcher' which selects, from a set of tasksgenerally much larger than the number of physical cores (or hardware threads),tasks that are ready for updating. The definition of a task can vary, forexample, with some solving the equations of ideal magnetohydrodynamics (MHD),others non-ideal MHD, radiative transfer, or particle motion, and yet othersapplying particle-in-cell (PIC) methods. Tasks do not have to be grid-based,while tasks that are, may use either Cartesian or orthogonal curvilinearmeshes. Patches may be stationary or moving. Mesh refinement can be static ordynamic. A feature of decisive importance for the overall performance of theframework is that time steps are determined and applied locally; this allowspotentially large reductions in the total number of updates required in caseswhen the signal speed varies greatly across the computational domain, andtherefore a corresponding reduction in computing time. Another feature is aload balancing algorithm that operates `locally' and aims to simultaneouslyminimise load and communication imbalance. The framework generally relies onalready existing solvers, whose performance is augmented when run under theframework, due to more efficient cache usage, vectorisation, localtime-stepping, plus near-linear and, in principle, unlimited OpenMP and MPIscaling.

DISPATCH: A Numerical Simulation Framework for the Exa-scale Era. I. Fundamentals