TTDFT: A GPU accelerated Tucker tensor DFT code for large-scale Kohn-Sham DFT calculations

Abstract

We present the Tucker tensor DFT (TTDFT) code which uses a tensor-structured algorithm with graphic processing unit (GPU) acceleration for conducting ground-state DFT calculations on large-scale systems. The Tucker tensor DFT algorithm uses a localized Tucker tensor basis computed from an additive separable approximation to the Kohn-Sham Hamiltonian. The discrete Kohn-Sham problem is solved using Chebyshev filtered subspace iteration method that relies on matrix-matrix multiplications of a sparse symmetric Hamiltonian matrix and a dense wavefunction matrix, expressed in the localized Tucker tensor basis. These matrix-matrix multiplication operations, which constitute the most computationally intensive step of the solution procedure, are GPU accelerated providing ∼8-fold GPU-CPU speedup for these operations on the largest systems studied. The computational performance of the TTDFT code is presented using benchmark studies on aluminum nano-particles and silicon quantum dots with system sizes ranging up to ∼7,000 atoms. Program summaryProgram Title: TTDFT: Tucker tensor density functional theory codeCPC Library link to program files:https://doi.org/10.17632/8dgmcs8ys2.1Licensing provisions: LGPLProgramming language: C/C++External routines/libraries: TuckerMPI (https://gitlab.com/tensors/TuckerMPI), cuBLAS (https://docs.nvidia.com/cuda/cublas/index.html), cuSparse (https://docs.nvidia.com/cuda/cusparse/index.html), ALGLIB (http://www.alglib.net/), Boost (https://www.boost.org/), BLAS (http://www.netlib.org/blas/), LAPACK (http://www.netlib.org/lapack/), PETSc (https://www.mcs.anl.gov/petsc), SLEPc (http://slepc.upv.es)Nature of problem: Real-space Kohn-Sham density functional theory calculations using localized Tucker tensor basis.Solution method: We present a real-space Kohn-Sham density functional theory code based on tensor-structured techniques with GPU acceleration. Tensor-structured techniques are adopted for computing a Tucker tensor basis, representing the eigenfunctions of an additive separable approximation to the Kohn-Sham Hamiltonian. The Tucker tensor basis is further localized using L1 regularization to improve the sparsity of the Kohn-Sham Hamiltonian matrix, and improve the computational efficiency and parallel scalability of the proposed algorithm. The solution to the Kohn-Sham problem in the localized Tucker tensor basis is computed using the Chebyshev filtered subspace iteration (ChFSI) method.Additional comments including restrictions and unusual features: The code works with Troullier-Martin (TM) pseudopotentials in Kleinman-Bylander form. The current release supports only non-periodic DFT calculations with the local density approximation (LDA) for exchange-correlation functional.This TTDFT project uses GitHub via Git, a free distributed version control software. The archived version at the time of submission of this work can be found on the CPC program library through program files DOI provided above. The GitHub repository of this project can be found on https://github.com/ttdftdev/ttdft_public.