Algorithms and Software Infrastructure for High-Performance Electronic Structure Based Simulations

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Computer simulations based on electronic structure theory, particularly Kohn-Sham density-functional theory (KS-DFT), are facilitating scientific discoveries across a broad range of disciplines such as chemistry, physics, and materials science. The tractable size of KS-DFT is often limited by an algebraic eigenproblem, the computational cost of which scales cubically with respect to the problem size. There have been continuous efforts to improve the performance of eigensolvers, and develop alternative algorithms that bypass the explicit solution of the eigenproblem. As the number of algorithms grows, it becomes increasingly difficult to comparatively assess their relative computational cost and implement them efficiently in electronic structure codes.

The research in this dissertation explores the feasibility of integrating different electronic structure algorithms into a single framework, combining their strengths, assessing their accuracy and computational cost relative to each other, and understanding their scope of applicability and optimal use regime. The research has led to an open-source software infrastructure, ELSI, providing the electronic structure community with access to a variety of high-performance solver libraries through a unified software interface. ELSI supports and enhances conventional cubic scaling eigensolvers, linear scaling density-matrix-based algorithms, and other reduced scaling methods in between, with reasonable default parameters for each of them. Flexible matrix formats and parallelization strategies adopted in ELSI fit the need of most, if not all, electronic structure codes. ELSI has been connected to four electronic structure code projects, allowing us to rigorously benchmark the performance of the solvers on an equal footing. Based on the results of a comprehensive set of benchmarks, we identify factors that strongly affect the efficiency of the solvers and regimes where conventional cubic scaling eigensolvers are outperformed by lower scaling algorithms. We propose an automatic decision layer that assists with the algorithm selection process.

The ELSI infrastructure is stimulating the optimization of existing algorithms and the development of new ones. Following the worldwide trend of employing graphical processing units (GPUs) in high-performance computing, we have developed and optimized GPU acceleration in the two-stage tridiagonalization eigensolver ELPA2, targeting distributed-memory, hybrid CPU-GPU architectures. A significant performance boost over the CPU-only version of ELPA2 is achieved, as demonstrated in routine KS-DFT simulations comprising thousands of atoms, for which a couple of GPU-equipped supercomputer nodes reach the throughput of some tens of conventional CPU supercomputer nodes. The GPU-accelerated ELPA2 solver can be used through the ELSI interface, smoothly and transparently bringing GPU support to all the electronic structure codes connected with ELSI. To reduce the computational cost of systems containing heavy elements, we propose a frozen core approximation with proper orthonormalization of the wavefunctions. This method is tolerant of errors due to the finite precision of numerical integrations in electronic structure codes. A considerable saving in the computational cost can be achieved, with the electron density, energies, and forces all matching the accuracy of all electron calculations.

This research shows that by integrating a broad range of electronic structure algorithms into one infrastructure, new algorithmic developments and optimizations can take place at a faster pace. The outcome is open and beneficial to the entire electronic structure community, instead of being restricted to one particular code project. The ELSI infrastructure has already been utilized to accelerate large-scale electronic structure simulations, some of which were not feasible before.





Yu, Wenzhe (2020). Algorithms and Software Infrastructure for High-Performance Electronic Structure Based Simulations. Dissertation, Duke University. Retrieved from


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