An Efficient Parallelization of the Accelerated Imaginary Time Step Method for the Static Hartree-Fock Problem
Leedom, Noah
Leedom, Noah
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Abstract
The simulation of quantum many-body systems is known to be computationally difficult. In the search for efficient methods by which to simulate systems of absorbed bosons which interact with each other and with an external potential, the iterative solver known as the Accelerated Imaginary Time Step Method (AITEM) was produced. While AITEM boasts several advantages over the regularly used Quantum Monte Carlo approach, the still significant runtime of the algorithm meant that further work was needed to maximize the efficiency of the solver. We develop a parallelized version of AITEM that addresses these computational difficulties. We utilize a wavefunction partitioning scheme which allows certain calculations to be done simultaneously per core. Additionally, since the simulation of any one particle depends on the effects of the other particles in the system, we have devised efficient methods by which cores may pass information between each other while minimizing the computational overhead incurred by this communication. A series of numerical experiments were run on the new solver to test its speed and robustness. The parallelized AITEM algorithm was run for three different sizes of the simulation. For each of these sizes, the solver was run with varying numbers of cores. This allowed us to test the scalability of the algorithm with respect to the number of particles and with respect to the number of cores. We found that parallelized AITEM outperformed the serial algorithm significantly. The speedup factor of parallelized AITEM increased as the number of cores increased. In the best case, we observed a two-times speedup when run on a standard PC and a seven-times speedup when run on the Vermont Advanced Computing Cluster. The optimal range of core numbers to avoid saturation of the parallelization is also provided.
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Date
1/1/2026
Student Status
Graduate Student
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Oral Presentation
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Applied Mathematics
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College of Engineering and Mathematical Sciences
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Mathematical Science