SplitSolve: A fast solver for wave function based quantum transport simulations on accelerators

We present SplitSolve, a novel sparse solver dedicated to linear systems in ballistic quantum transport calculations. The proposed algorithm specifically addresses the need for higher performance in the innermost loop of the energy integration in ab-initio simulations on hybrid architectures. The computation of the open boundary condition is deserialized from the most time consuming preprocessing step of the linear solver. The implementation of the algorithm itself is based on algebraic primitives that perform close to peak performance on current accelerator platforms. Using SplitSolve it is possible to efficiently harness the computational performance of these devices for a specific class of sparse systems. Combined with an efficient eigenvalue solver for the open boundary conditions, CPUs and accelerators can be used in parallel, resulting in significant speedups and much increased resource usage compared to traditional CPU-based methods. We compare here our implementation of SplitSolve with MUMPS, a state-of-the-art sparse linear solver for CPUs, and demonstrate an overall speedup of 7.7× for a nanowire simulation.