Time-dependent density-functional theory in massively parallel computer architectures: the octopus project

Abstract

Octopus is a general-purpose density-functional theory (DFT) code, with a particular emphasis on the time-dependent version of DFT (TDDFT). In this article we present the ongoing efforts for the parallelisation of octopus. We focus on the real-time variant of TDDFT, where the time-dependent Kohn-Sham equations are directly propagated in time. This approach has a great potential for execution in massively parallel systems such as modern supercomputers with thousands of processors and graphics processing units (GPUs).For harvesting the potential of conventional supercomputers, the main strategy is a multilevel parallelisation scheme that combines the inherent scalability of real-time TDDFT with a real-space grid domain-partitioning approach. A scalable Poisson solver is critical for the efficiency of this scheme. For GPUs, we show how using blocks of Kohn-Sham states * xavier@tddft.org 60 provides the required level of data-parallelism and that this strategy is also applicable for code-optimisation on standard processors. Our results show that real-time TDDFT, as implemented in octopus, can be the method of choice to study the excited states of large molecular systems in modern parallel architectures.

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

“…(D1). If we further restrict the modes by introducing a square-summable regularization function f EM ( n), 13 e.g., f EM = 1 for | n| < mcL/ (2π ) (energy smaller than rest-mass energy) and 0 otherwise, the resulting regularized field…”

“…Especially density-functional theories, which are based on the simplest of those (functional) variables, the one-particle density (current), have proven to be exceptionally successful [11]. Their success can be attributed to the unprecedented balance between accuracy and numerical feasibility [12], which allows us at present to treat several thousands of atoms [13]. Although the different flavors of density-functional theories cover most of the traditional problems of physics and chemistry (including approaches that combine classical Maxwell dynamics with the quantum particles [14][15][16][17][18]), by construction these theories can not treat problems involving the quantum nature of light.…”

Performance of Nonlocal Optics When Applied to Plasmonic Nanostructures

“…25 Regarding the quantum simulations, we use the Octopus package in which the TD-DFT equations are solved in real space and time domains. [40][41][42] We have implemented the translational symmetry of the nanowires in Octopus for both static (ground state) and time-dependent calculations by imposing periodic Born-von Kár-mán boundary conditions on the Z direction (no supercell is defined on the XY plane since Octopus is a real-space code).…”

Graphics Processing Unit acceleration of the Random Phase Approximation in the projector augmented wave method

“…An increasing number of scientific applications have been ported to GPUs [22]. In particular, for electronic structure calculations, GPUs have been utilized for many quantum chemistry and DFT codes such as gpaw [23], vasp [24,25], quantum espresso [26], terachem [27], bigdft [28], petot [29] and octopus [30]. The speed up of these DFT-based electronic structure codes is generally less than 15× due to the complexity and communication bottlenecks in algorithms such as FFT, subspace diagonaliza-tion, minimization and orbital orthorgonalization.…”