Related papers: An Optimized and Scalable Eigensolver for Sequence…
In one of the most important methods in Density Functional Theory - the Full-Potential Linearized Augmented Plane Wave (FLAPW) method - dense generalized eigenproblems are organized in long sequences. Moreover each eigenproblem is strongly…
Solving dense Hermitian eigenproblems arranged in a sequence with direct solvers fails to take advantage of those spectral properties which are pertinent to the entire sequence, and not just to the single problem. When such features take…
Studying the optoelectronic structure of materials can require the computation of several thousands of the smallest positive eigenpairs of a pseudo-hermitian Hamiltonian. Iterative eigensolvers may be preferred over direct methods for this…
As modern massively parallel clusters are getting larger with beefier compute nodes, traditional parallel eigensolvers, such as direct solvers, struggle keeping the pace with the hardware evolution and being able to scale efficiently due to…
We consider the problem of parallelizing electronic structure computations in plane-wave Density Functional Theory. Because of the limited scalability of Fourier transforms, parallelism has to be found at the eigensolver level. We show how…
In Density Functional Theory simulations based on the LAPW method, each self-consistent field cycle comprises dozens of large dense generalized eigenproblems. In contrast to real-space methods, eigenpairs solving for problems at distinct…
Chebyshev Filtered Subspace Iteration (ChFSI) is widely used for computing a small subset of extremal eigenpairs from large matrices, particularly when the eigenpairs must be computed repeatedly as the system matrix evolves within an outer…
As supercomputers become larger with powerful Graphics Processing Unit (GPU), traditional direct eigensolvers struggle to keep up with the hardware evolution and scale efficiently due to communication and synchronization demands.…
Interior eigenvalue problems for large-scale sparse Hermitian matrices are fundamental in computational science. We propose an adaptive polynomial filtering strategy based on Chebyshev expansion of a step function, integrated into a…
Solving the Kohn-Sham eigenvalue problem constitutes the most computationally expensive part in self-consistent density functional theory (DFT) calculations. In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace…
In this paper, by introducing a class of relaxed filtered Krylov subspaces, we propose the relaxed filtered Krylov subspace method for computing the eigenvalues with the largest real parts and the corresponding eigenvectors of non-symmetric…
We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is…
Eigenvalue problems are among the most important topics in many scientific disciplines. With the recent surge and development of machine learning, neural eigenvalue methods have attracted significant attention as a forward pass of inference…
We develop a distributed Block Chebyshev-Davidson algorithm to solve large-scale leading eigenvalue problems for spectral analysis in spectral clustering. First, the efficiency of the Chebyshev-Davidson algorithm relies on the prior…
The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…
We examine and compare several iterative methods for solving large-scale eigenvalue problems arising from nuclear structure calculations. In particular, we discuss the possibility of using block Lanczos method, a Chebyshev filtering based…
A type of parallel augmented subspace scheme for eigenvalue problems is proposed by using coarse space in the multigrid method. With the help of coarse space in multigrid method, solving the eigenvalue problem in the finest space is…
This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…
A parallel implementation of an eigensolver designed for electronic structure calculations is presented. The method is applicable to computational tasks that solve a sequence of eigenvalue problems where the solution for a particular…