Chebyshev polynomial filtered subspace iteration in the discontinuous Galerkin method for largescale electronic structure calculations
Abstract
The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the KohnSham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated onthefly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for largescale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in largescale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a twodimensional parallelization scheme, thanks to the orthogonality of the DG basis set and blocksparse structure of the DG Hamiltonian matrix. The onthefly nature of the ALB functions requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DGCheFSI approach in calculations of largescale twodimensional graphene sheets and bulk threedimensional lithiumion electrolyte systems. Employing 55 296 computational cores, the time per selfconsistent field iteration for a sample of the bulk 3D electrolyte containing 8586 atoms is 90 s, and the time for a graphene sheet containing 11 520 atoms is 75 s.
 Publication:

Journal of Chemical Physics
 Pub Date:
 October 2016
 DOI:
 10.1063/1.4964861
 arXiv:
 arXiv:1606.03416
 Bibcode:
 2016JChPh.145o4101B
 Keywords:

 Physics  Computational Physics;
 Condensed Matter  Materials Science
 EPrint:
 Submitted to The Journal of Chemical Physics