Related papers: High Performance Solution of Skew-symmetric Eigenv…

The solution of (generalized) eigenvalue problems for symmetric or Hermitian matrices is a common subtask of many numerical calculations in electronic structure theory or materials science. Solving the eigenvalue problem can easily amount…

Optical properties of materials related to light absorption and scattering are explained by the excitation of electrons. The Bethe-Salpeter equation is the state-of-the-art approach to describe these processes from first principles (ab…

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…

Large-scale eigenvalue computations on sparse matrices are a key component of graph analytics techniques based on spectral methods. In such applications, an exhaustive computation of all eigenvalues and eigenvectors is impractical and…

Optimally hybrid numerical solvers were constructed for massively parallel generalized eigenvalue problem (GEP).The strong scaling benchmark was carried out on the K computer and other supercomputers for electronic structure calculation…

The solution of eigenproblems is often a key computational bottleneck that limits the tractable system size of numerical algorithms, among them electronic structure theory in chemistry and in condensed matter physics. Large eigenproblems…

SLEPc is a parallel library for the solution of various types of large-scale eigenvalue problems. In the last years we have been developing a module within SLEPc, called NEP, that is intended for solving nonlinear eigenvalue problems. These…

Large symmetric eigenvalue problems are commonly observed in many disciplines such as Chemistry and Physics, and several libraries including cuSOLVERMp, MAGMA and ELPA support computing large eigenvalue decomposition on multi-GPU or…

We present a framework to solve non-linear eigenvalue problems suitable for a Finite Element discretization. The implementation is based on the open-source finite element software GetDP and the open-source library SLEPc. As template…

The last ten years have witnessed fast spreading of massively parallel computing clusters, from leading supercomputing facilities down to the average university computing center. Many companies in the private sector have undergone a similar…

The Bethe-Salpeter eigenvalue problem is a structured eigenvalue problem arising in many-body physics. In practice, a few of the smallest positive eigenvalues and the corresponding eigenvectors need to be computed. In principle, the LOBPCG…

We present a massively parallel, GPU-accelerated implementation of the Bethe-Salpeter equation (BSE) for the calculation of the vertical excitation energies (VEEs) and optical absorption spectra of condensed and molecular systems, starting…

We propose a new method for computing the eigenvalue decomposition of a dense real normal matrix $A$ through the decomposition of its skew-symmetric part. The method relies on algorithms that are known to be efficiently implemented, such as…

In this paper, we study and implement the structural iterative eigensolvers for the large-scale eigenvalue problem in the Bethe-Salpeter equation (BSE) based on the reduced basis approach via low-rank factorizations in generating matrices,…

We introduce a new collection of solvers - subsequently called EleMRRR - for large-scale dense Hermitian eigenproblems. EleMRRR solves various types of problems: generalized, standard, and tridiagonal eigenproblems. Among these, the last is…

Many large-scale scientific computations require eigenvalue solvers in a scaling regime where efficiency is limited by data movement. We introduce a parallel algorithm for computing the eigenvalues of a dense symmetric matrix, which…

Current dense symmetric eigenvalue (EIG) and singular value decomposition (SVD) implementations may suffer from the lack of concurrency during the tridiagonal and bidiagonal reductions, respectively. This performance bottleneck is typical…

An open-source middleware EigenKernel was developed for use with parallel generalized eigenvalue solvers or large-scale electronic state calculation to attain high scalability and usability. The middleware enables the users to choose the…

The Bethe-Salpeter eigenvalue problem is a dense structured eigenvalue problem arising from discretized Bethe-Salpeter equation in the context of computing exciton energies and states. A computational challenge is that at least half of the…

In this paper, a Parallel Direct Eigensolver for Sequences of Hermitian Eigenvalue Problems with no tridiagonalization is proposed, denoted by \texttt{PDESHEP}, and it combines direct methods with iterative methods. \texttt{PDESHEP} first…