Matrix-free multi-GPU Implementation of Elliptic Solvers for strongly anisotropic PDEs

Manycore chip architectures such as Graphics Processing Units (GPUs) have been shown to be highly e cient both in terms of total performance and small power consumption in many areas of Scientific Computing. However, implementing memory-bound applications such as elliptic solvers for large partial di↵erential equations (PDEs) remains a challenge. We consider iterative solvers for strongly anisotropic PDEs which arise in many problems in geophysical modelling in “flat” domains, such as numerical weatherand climate prediction (NWP), global ocean models or subsurface reservoirand flowsimulations. For example, an equation for the pressure correction has to be solved in a thin spherial shell representing the earth’s atmosphere at every timestep in many NWP codes. To improve the accuracy of the model, the spatial resolution is continuously increased and this leads to significant computational challenges as forecasts have to be delivered on operational timescales.