Related papers: Parallel eigensolvers in plane-wave Density Functi…
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…
In many scientific applications the solution of non-linear differential equations are obtained through the set-up and solution of a number of successive eigenproblems. These eigenproblems can be regarded as a sequence whenever the solution…
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…
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…
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…
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…
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our…
We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantages of 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…
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…
Chebyshev filter diagonalization is well established in quantum chemistry and quantum physics to compute bulks of eigenvalues of large sparse matrices. Choosing a block vector implementation, we investigate optimization opportunities on the…
We address the communication overhead of distributed sparse matrix-(multiple)-vector multiplication in the context of large-scale eigensolvers, using filter diagonalization as an example. The basis of our study is a performance model which…
Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method…
We propose an adaptive planewave method for eigenvalue problems in electronic structure calculations. The method combines a priori convergence rates and accurate a posteriori error estimates into an effective way of updating the energy…
Motivated by the recently proposed parallel orbital-updating approach in real space method, we propose a parallel orbital-updating based plane-wave basis method for electronic structure calculations, for solving the corresponding eigenvalue…
This paper concerns the design of a multidimensional Chebyshev interpolation based method for a differential game theory problem. In continuous game theory problems, it might be difficult to find analytical solutions, so numerical methods…
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…
A linear-algebraic theory called 'multiple Arnoldi method' is presented and realizes large-scale (order-N) electronic structure calculation with generalized eigen-value equations. A set of linear equations, in the form of (zS-H) x = b, are…
Unions of graph Fourier multipliers are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators to the high-dimensional signals…
Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes ($\lesssim$ 5000), performance of traditional dense diagonalization algorithms on…