High Performance Solution of Skew-symmetric Eigenvalue Problems with Applications in Solving the Bethe-Salpeter Eigenvalue Problem

Abstract

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.

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Cited by in corpus (5)

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• A skew-symmetric Lanczos bidiagonalization method for computing several largest eigenpairs of a large skew-symmetric matrix
• Solvers for the Hermitian and the pseudo-Hermitian Bethe-Salpeter equation in the Yambo code: Implementation and Performance
• A generalized skew-symmetric Lanczos bidiagonalization method for computing several extreme eigenpairs of a large skew-symmetric/symmetric positive definite matrix pair
• Parallel-in-time preconditioners for the Sinc-Nyström method