Related papers: A Bi-Orthogonal Structure-Preserving eigensolver f…
We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity…
We introduce an eigenvalue-preserving transformation algorithm from the generalized eigenvalue problem by matrix pencil of the upper and the lower bidiagonal matrices into a standard eigenvalue problem while preserving sparsity, using the…
The use of spectral projection based methods for simulation of a stochastic system with discontinuous solution exhibits the Gibbs phenomenon, which is characterized by oscillations near discontinuities. This paper investigates a dynamic…
We present a hybrid OpenMP/Charm++ framework for solving the $\mathcal{O} (N)$ Self-Consistent-Field eigenvalue problem with parallelism in the strong scaling regime, $P\gg{N}$, where $P$ is the number of cores, and $N$ a measure of system…
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…
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…
This review discusses progress in efficient solvers which have as their foundation a representation in real space, either through finite-difference or finite-element formulations. The relationship of real-space approaches to linear-scaling…
The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…
The adoption of hybrid GPU-CPU nodes in traditional supercomputing platforms opens acceleration opportunities for electronic structure calculations in materials science and chemistry applications, where medium sized Hermitian generalized…
In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…
In this paper, we present a novel parallel augmented subspace method and build a package Parallel Augmented Subspace Eigensolver (PASE) for solving large scale eigenvalue problems by the massively parallel finite element discretization.…
The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural…
A novel orthogonalization-free method together with two specific algorithms are proposed to solve extreme eigenvalue problems. On top of gradient-based algorithms, the proposed algorithms modify the multi-column gradient such that earlier…
The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems that are based on a reduction to…
Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…
We present numerical upscaling techniques for a class of linear second-order self-adjoint elliptic partial differential operators (or their high-resolution finite element discretization). As prototypes for the application of our theory we…
In \emph{Wang et al., A Shifted Laplace Rational Filter for Large-Scale Eigenvalue Problems}, the SLRF method was proposed to compute all eigenvalues of a symmetric definite generalized eigenvalue problem lying in an interval on the real…
This paper presents a new algorithm for the parallel in time (PiT) numerical simulation of time dependent partial/ordinary differential equations. We propose a reliable alternative to the well know parareal in time algorithm, by formulating…
In this paper, a scalable iterative projection-type algorithm for solving non-stationary systems of linear inequalities is considered. A non-stationary system is understood as a large-scale system of inequalities in which coefficients and…
This paper proposes a novel computationally efficient dynamic bi-orthogonality based approach for calibration of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on a…