We analyze the performance of two strategies in solving the structured eigenvalue problem deriving from the Bethe-Salpeter equation (BSE) in condensed matter physics. The BSE matrix is constructed with the Yambo code, and the two strategies are implemented by interfacing Yambo with the ScaLAPACK and ELPA libraries for direct diagonalization, and with the SLEPc library for the iterative approach. We consider both the Hermitian (Tamm-Dancoff approximation) and pseudo-Hermitian forms, addressing dense matrices of three different sizes. A description of the implementation is also provided, with details for the pseudo-Hermitian case. Timing and memory utilization are analyzed on both CPU and GPU clusters. Our results demonstrate that it is now feasible to handle dense BSE matrices of the order of 10^5.

翻译：本文分析了凝聚态物理中求解Bethe-Salpeter方程（BSE）导出结构化特征值问题的两种计算策略的性能。BSE矩阵通过Yambo代码构建，两种策略分别通过以下方式实现：将Yambo与ScaLAPACK和ELPA库对接进行直接对角化，以及与SLEPc库对接进行迭代求解。我们同时考虑了厄米形式（Tamm-Dancoff近似）和伪厄米形式，并针对三种不同规模的稠密矩阵进行计算。文中还详细描述了实现方案，特别对伪厄米情形进行了说明。我们在CPU和GPU集群上分析了计算时间与内存使用情况。结果表明，当前已能处理规模达10^5量级的稠密BSE矩阵。