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.

中文翻译：

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用于研究狄拉克和拓扑材料的电子特性的特定领域语言和无矩阵模板代码

我们介绍了 PVSC-DTM（Dirac 和拓扑材料的并行矢量化模板代码），这是一个基于领域特定语言的库和代码生成器，用于实现可以描述 Dirac 和拓扑材料（如石墨烯和拓扑材料）的特定模板类算法。以无矩阵的方式绝缘体。生成的混合并行 (MPI+OpenMP) 代码使用单指令多数据 (SIMD) 扩展完全矢量化。在节点级别，它比基于矩阵的方法快得多，并且按照屋顶线模型执行。我们展示了基本构建块（例如现代多核 CPU 上的稀疏矩阵（多个）向量乘法）的芯片级性能和分布式内存可扩展性。作为应用示例，