We examine the computational aspects of propagating a global R-matrix, ℜ, across sub-regions in a 2-D plane. This problem originates in the large scale simulation of electron collisions with atoms and ions at intermediate energies. The propagation is dominated by matrix multiplications which are complicated because of the dynamic nature of ℜ, which changes the designations of its rows and columns and grows in size as the propagation proceeds. The use of PBLAS to solve this problem on distributed memory HPC machines is the main focus of the paper. Topics: Large Scale Simulations in all areas of Engineering and Science; Numerical Methods; Parallel and Distributed Computing.