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The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are…
In this paper, we propose an efficient parallelization strategy for boundary element method (BEM) solvers that perform the electromagnetic analysis of structures with lossy conductors. The proposed solver is accelerated with the adaptive…
Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum…
Unions of graph multiplier operators 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. The proposed method features…
The Poisson pressure solve resulting from the spectral element discretization of the incompressible Navier-Stokes equation requires fast, robust, and scalable preconditioning. In the current work, a parallel scaling study of…
Electromagnetic computations, where the wavelength is small in relation to the geometry of interest, become computationally demanding. In order to manage computations for realistic problems like electromagnetic scattering from aircraft, the…
The purpose of this work is to study spectral methods to approximate the eigenvalues of nonlocal integral operators. Indeed, even if the spatial domain is an interval, it is very challenging to obtain closed analytical expressions for the…
A new method of solution to the local spin density approximation to the electronic Schr\"{o}dinger equation is presented. The method is based on an efficient, parallel, adaptive multigrid eigenvalue solver. It is shown that adaptivity is…
We discuss a numerical algorithm for solving nonlinear integro-differential equations, and illustrate our findings for the particular case of Volterra type equations. The algorithm combines a perturbation approach meant to render a…
We suggest and implement a parallelization scheme based on an efficient multiband eigenvalue solver, called the locally optimal block preconditioned conjugate gradient LOBPCG method, and using an optimized three-dimensional (3D) fast…
The problem of solving a system of polynomial equations is one of the most fundamental problems in applied mathematics. Among them, the problem of solving a system of binomial equations form a important subclass for which specialized…
Efficient and stable algorithms for the calculation of spectral quantities and correlation functions are some of the key tools in computational condensed matter physics. In this article we review basic properties and recent developments of…
Exponential divided differences arise in numerical linear algebra, matrix-function evaluation, and quantum Monte Carlo simulations, where they serve as kernel weights for time evolution and observable estimation. Efficient and numerically…
The vertical modes of linearized equations of motion are widely used by the oceanographic community in numerous theoretical and observational contexts. However, the standard approach for solving the generalized eigenvalue problem using…
A new algorithm for Monte Carlo calculation of the double exchange model is studied. The algorithm is commonly applicable to wide classes of strongly correlated electron systems which involve itinerant electrons coupled with…
In this paper, we assess the performance of adaptive and nested factorized sparse approximate inverses as smoothers in multilevel V-cycles, when smoothing is performed following the Chebyshev iteration of the fourth kind. For our test…
We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decomposition. Algorithms for solving polynomial systems combine low-level routines for performing arithmetic operations on…
In this article, we present a parallel recursive algorithm based on multi-level domain decomposition that can be used as a precondtioner to a Krylov subspace method to solve sparse linear systems of equations arising from the discretization…
We present a plane-wave ultrasoft pseudopotential implementation of first-principle molecular dynamics, which is well suited to model large molecular systems containing transition metal centers. We describe an efficient strategy for…
The real-space density-functional perturbation theory (DFPT) for the computations of the response properties with respect to the atomic displacement and homogeneous electric field perturbation has been recently developed and implemented…