Parallelization of R-matrix propagation methods on distributed memory computers

The R-matrix and Logarithmic Derivative methods are numerically very stable and are therefore ideal for integrating the large sets of coupled second-order linear differential equations which arise in non-exchange scattering problems (e.g., electron scattering by atoms and molecules). These calculations, which typically are repeated at many scattering energies, can become computationally demanding requiring the use of massively parallel computers. Here the results of a study of various parallel decompositions of typical R-matrix propagator methods are reported. A data decomposition approach is employed in the solution following Baluja-Burke-Morgan method whereas a hybrid approach, involving both control and domain decomposition, is adopted for the potential following Light-Walker method. Timings of test computations obtained using a Cray T3D computer demonstrate that R-matrix external region computations involving between 500 and 1500 scattering channels are feasible. The approach is easily extended to much larger calculations and to other computer architectures.