2019/12/31 by Carolin Penke, Andreas Marek, Christian Vorwerk +2 · 14 citations
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Bethe–Salpeter equation #Computational science #Computer science #Divide-and-conquer eigenvalue algorithm #Eigenvalues and eigenvectors #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Molecular spectroscopy and chirality #Physics #Quantum mechanics #Scalability #Skew #Solver #Spectroscopy and Quantum Chemical Studies #acm:15B57 #acm:65Y05 #cs.DS #cs.MS #cs.NA #math.NA #msc:15B57 #msc:65Y05
paper · pdf · doi:10.1016/j.parco.2020.102639
published in Parallel Computing 96, 102639 (Elsevier BV)
arxiv created 2020/04/20 · openalex publication_date 2020/04/30 · arxiv updated 2020/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a high-performance solver for dense skew-symmetric matrix eigenvalue problems. Our work is motivated by applications in computational quantum physics, where one solution approach to solve the so-called Bethe-Salpeter equation involves the solution of a large, dense, skew-symmetric eigenvalue problem. The computed eigenpairs can be used to compute the optical absorption spectrum of molecules and crystalline systems. One state-of-the art high-performance solver package for symmetric matrices is the ELPA (Eigenvalue SoLvers for Petascale Applications) library. We extend the methods available in ELPA to skew-symmetric matrices. This way, the presented solution method can benefit from the optimizations available in ELPA that make it a well-established, efficient and scalable library, such as GPU support. We compare performance and scalability of our method to the only available high-performance approach for skew-symmetric matrices, an indirect route involving complex arithmetic. In total, we achieve a performance that is up to 3.67 higher than the reference method using Intel's ScaLAPACK implementation. The runtime to solve the Bethe-Salpeter-Eigenvalue problem can be improved by a factor of 10. Our method is freely available in the current release of the ELPA library.