Multi-Layered MPI parallelisation for the R-matrix with time-dependence code.

The R-matrix with Time Dependence code package RMT is a numerical solver for the time- dependent Schrödinger equation. As such it provides a means for describing the time-domain behaviour of atomic and molecular systems driven by external fields. RMT is at the forefront of research in attosecond/ultrafast/strong-field physics wherein it is the only code capable of describing general systems driven by arbitrarily polarised laser pulses, with a full account of the multi-electron correlation. RMT employs the R-matrix division-of-space principle. The physical space occupied by the electronic wavefunction is divided into two distinct regions. In the inner region, centred on the nuclear centre of mass, multielectron effects are described in full. In the outer region, an ionised electron is sufficiently isolated from the residual ion that electron exchange with the residual electrons can be neglected. In the small inner region, a basis set expansion is used to give an accurate description of the multielectron correlation, while in the large outer region the one-electron wavefunction is described on a finite-difference grid. This eCSE project has added new levels to the separate existing MPI parallelization schemes in the two regions. The inner region parallelization was restricted to at least 1 task per component symmetry: it now allows several symmetries per task, so that the number of inner region tasks can be much smaller than before in appropriate calculations. The outer region parallelization allowed for 1 task per radial sector of grid points. It now allows for several tasks per sector, dividing up the wavefunction component ‘channels’ among them. An existing option for OpenMP parallelization over channels handled by a task is retained. Performance improvements on ARCHER2 are illustrated, and a systematic approach for choosing the correct balance of inner- and outer-region tasks for large and costly calculations is given.