First-Principles Molecular Dynamics (FPMD) methods, although powerful, are computationally very expensive due to the quantum modeling of electrons. Traditional FPMD approaches have typically been limited to a few thousand atoms at most, due to O(N<sup>3</sup>) or worse solver complexity and the large amount of communication required for highly parallel implementations. Attempts to reduce computational complexity have often introduced uncontrolled approximations or systematic errors. Using a combination of new algorithms, including a real-space discretization with localization constraints and a parallel sparse linear algebra solver specifically designed for matrices whose inverses have fast-decaying off-diagonal elements, we have developed an O(N) complexity solver for electronic structure problems with fully controllable numerical error. Its minimal use of global communications yields excellent weak scalability, allowing for very accurate FPMD simulations of more than a million atoms on over a million cores. At these scales, this approach provides multiple orders of magnitude speedup compared to the standard plane-wave approach typically used in condensed matter applications, without sacrificing accuracy. Challenges remain to speedup time-to-solution, as well as in making the algorithm more robust for long molecular dynamics.<br/>

First-principles molecular dynamics: Computing more than a million atoms with over a million cores

254th National Meeting (2017)

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