Frequency Parallelization of the Inverse Dielectric Matrix in the BerkeleyGW Code

Derek Vigil Currey, Ohio Supercomputer Center

Usage Details

The calculation of band gaps and other excited-state properties of materials of fundamental and technological interest requires calculating the dielectric matrix (DM) of the system and inverting it to give the inverse dielectric matrix (IDM). These matrices are frequency dependent, scale with system size, and are in general quite large, especially for many systems of increasing interest, e.g. reduced-dimensional systems. Currently the BerkeleyGW (BGW) code, is very well parallelized for calculating the DM, scaling up to tens of thousands of processors. However, for the matrix inversion BGW currently uses ScaLAPACK, which scales to roughly 50 processors. This results in wasted computational resources, as the additional processors past 50 used for the calculation of the DM give no benefit for the matrix inversion. To solve this problem, I will exploit the frequency dependence of the DM to add a layer of parallelism to the calculation of the DM/IDM. BGW currently calculates the DM/IDM one frequency at a time, while the algorithm I will implement instead calculates multiple frequencies at once. Since DMs at multiple frequencies will be inverted to yield IDMs this will relieve the ScaLAPACK bottleneck. This will allow BGW to scale up to larger systems and will allow researchers to study all types of systems with much improved computational efficiency and speed.