Parallel adaptive quantum trajectory method for wavepacket simulations

Time-dependent wavepackets are widely used to model various phenomena in physics. One approach in simulating the wavepacket dynamics is the quantum trajectory method (QTM). Based on the hydrodynamic formulation of quantum mechanics, the QTM represents the wavepacket by an unstructured set of pseudoparticles whose trajectories are coupled by the quantum potential. The governing equations for the pseudoparticle trajectories are solved using a computationally intensive moving weighted least squares (MWLS) algorithm, and the trajectories can be computed in parallel. This paper contributes a strategy for improving the performance of wavepacket simulations using the QTM. Specifically, adaptivity is incorporated into the MWLS algorithm, and loop scheduling techniques are employed to dynamically load balance the parallel computation of the trajectories. The adaptive MWLS algorithm reduces the amount of computations without sacrificing accuracy, while adaptive loop scheduling addresses the load imbalance introduced by the algorithm and the runtime system. Results of experiments on a Linux cluster are presented to confirm that the adaptive MWLS reduces the trajectory computation time by up to 24%, and adaptive loop scheduling achieves parallel efficiencies of up to 85% when simulating a free particle.