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

摘要

We introduce PVSC-DTM, a highly parallel and SIMD-vectorized library and codegenerator based on a domain-specific language tailored to implement thespecific stencil-like algorithms that can describe Dirac and topologicalmaterials such as graphene and topological insulators in a matrix-free way. Thegenerated hybrid-parallel (MPI+OpenMP) code is significantly faster thanmatrix-based approaches on the node level and performs in accordance with theRoofline model. We demonstrate the chip-level performance anddistributed-memory scalability of basic building blocks such as sparsematrix-(multiple-) vector multiplication on modern multicore CPUs. As anapplication example, we use the PVSC-DTM scheme to (i) explore the scatteringof a Dirac wave on an array of gate-defined quantum dots, to (ii) calculate abunch of interior eigenvalues for strong topological insulators, and to (iii)discuss the photoemission spectra of a disordered Weyl semimetal.