相关论文: FEAST fundamental framework for electronic structu…

We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…

We have applied the Finite Element Method to the self-consistent electronic structure calculations of molecules and solids for the first time. In this approach all the calculations are performed in "real space" and the use of non-uniform…

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…

The design of cyber-physical systems is challenging in that it includes the analysis and synthesis of distributed and embedded real-time systems for controlling, often in a nonlinear way, the environment. We address this challenge with…

We propose a contour integral-based algorithm for computing a few singular values of a matrix or a few generalized singular values of a matrix pair. Mathematically, the generalized singular values of a matrix pair are the eigenvalues of an…

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…

Eigenvalue problems serve as fundamental substrates for applications in large-scale scientific simulations and machine learning, often requiring computation on massively parallel platforms. As these platforms scale to hundreds of thousands…

In (relativistic) electronic structure methods, the quaternion matrix eigenvalue problem and the linear response (Bethe-Salpeter) eigenvalue problem for excitation energies are two frequently encountered structured eigenvalue problems.…

The atomic norm provides a generalization of the $\ell_1$-norm to continuous parameter spaces. When applied as a sparse regularizer for line spectral estimation the solution can be obtained by solving a convex optimization problem. This…

We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…

The program FIESTA has been completely rewritten. Now it can be used not only as a tool to evaluate Feynman integrals numerically, but also to expand Feynman integrals automatically in limits of momenta and masses with the use of sector…

Generalized eigenvalue problems (GEPs) play an important role in the variety of fields including engineering, machine learning and quantum chemistry. Especially, many problems in these fields can be reduced to finding the minimum or maximum…

We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the…

In this paper, we propose an efficient numerical scheme for solving some large scale ill-posed linear inverse problems arising from image restoration. In order to accelerate the computation, two different hidden structures are exploited.…

We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…

This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…

In this work, we present a computationally efficient methodology that utilizes a local real-space formulation of the projector augmented wave (PAW) method discretized with a finite-element (FE) basis to enable accurate and large-scale…

A coarse-grained computational procedure based on the Finite Element Method is proposed to calculate the normal modes and mechanical response of proteins and their supramolecular assemblies. Motivated by the elastic network model, proteins…

The problem of quantum test is formally addressed. The presented method attempts the quantum role of classical test generation and test set reduction methods known from standard binary and analog circuits. QuFault, the authors software…

Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…