A domain-specific language and matrix-free stencil code for investigating electronic properties of Dirac and topological materials

TL;DR

This paper presents PVSC-DTM, a domain-specific language and code generator for efficient, matrix-free simulation of Dirac and topological materials, enabling faster and scalable computations on modern CPUs.

Contribution

Introduction of PVSC-DTM, a novel domain-specific language and code generator for matrix-free stencil algorithms tailored to topological materials, with demonstrated high performance and scalability.

Findings

Significantly faster than matrix-based approaches on CPUs.

Achieves high vectorization and parallel scalability.

Effectively models complex phenomena in topological materials.

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.