A domain-specific language and matrix-free stencil code for investigating electronic properties of Dirac and topological materials. (January 2021)

• Record Type: Journal Article
• Authors: Pieper, Andreas; Hager, Georg; Fehske, Holger
• Other Names: Wyrzykowski Roman guest-editor.; Deelman Ewa guest-editor.
• Is Part Of: International journal of high performance computing applications. Volume 35:Number 1(2021)
• Page Start: 60
• Page End: 77
• Publication Date: 2021-01
• Subjects: Stencil code -- domain-specific language -- topological quantum matter; High performance computing -- Periodicals; Supercomputers -- Periodicals; 004.1105
• DOI: 10.1177/1094342020959423
• Languages: English
• ISSNs: 1094-3420

Abstract

We introduce PVSC-DTM (Parallel Vectorized Stencil Code for Dirac and Topological Materials), a library and code generator based on a domain-specific language tailored to implement the specific stencil-like algorithms that can describe Dirac and topological materials such as graphene and topological insulators in a matrix-free way. The generated hybrid-parallel (MPI+OpenMP) code is fully vectorized using Single Instruction Multiple Data (SIMD) extensions. It is significantly faster than matrix-based approaches on the node level and performs in accordance with the roofline model. We demonstrate the chip-level performance and distributed-memory scalability of basic building blocks such as sparse matrix-(multiple-) vector multiplication on modern multicore CPUs. As an application example, we use the PVSC-DTM scheme to (i) explore the scattering of a Dirac wave on an array of gate-defined quantum dots, to (ii) calculate a bunch of interior eigenvalues for strong topological insulators, and to (iii) discuss the photoemission spectra of a disordered Weyl semimetal.