Solution of Few-Body Coulomb Problems with Latent Matrices on Multicore Processors

Abstract

We re-formulate a classical numerical method for the solution of systems of linear equations to tackle problems with latent data, that is, linear systems of dimension that is a priori unknown. This type of systems appears in the solution of few-body Coulomb problems for Atomic Simulation Physics, in the form of multidimensional partial differential equations (PDEs) that require the numerical solution of a sequence of recurrent dense linear systems of growing scale. The large dimension of these systems, with up to several hundred thousands of unknowns, is tackled in our approach via a task-parallel implementation of a solver based on the QR factorization. This method is parallelized using the OmpSs framework, showing fair strong and weak scalability on a multicore processor equipped with 12 Intel cores.