Related papers: Non-linear eigensolver-based alternative to tradit…

The Poisson-Boltzmann equation is widely used to model molecular electrostatics; however, it is usually solved in linearised form because the sinh nonlinearity is challenging, limiting its applicability in highly charged systems such as…

This paper proposes a homogeneous second-order descent framework (HSODF) for nonconvex and convex optimization based on the generalized homogeneous model (GHM). In comparison to the Newton steps, the GHM can be solved by extremal symmetric…

We introduce a new class of integrators for stiff ODEs as well as SDEs. These integrators are (i) {\it Multiscale}: they are based on flow averaging and so do not fully resolve the fast variables and have a computational cost determined by…

The FEAST eigenvalue algorithm is a subspace iteration algorithm that uses contour integration in the complex plane to obtain the eigenvectors of a matrix for the eigenvalues that are located in any user-defined search interval. By…

In this work, we present a new diagrammatic method for computing the effective Hamiltonian of driven nonlinear oscillators. At the heart of our method is a self-consistent perturbation expansion developed in phase space, which establishes a…

The paper proposes a method to obtain the optimal basis set for solving the self consistent field (SCF) equations for large atomic systems in order to calculate the energy barriers in tunneling structures, with higher accuracy and speed.…

We propose a natural application of Quantum Linear Systems Problem (QLSP) solvers such as the HHL algorithm to efficiently prepare highly excited interior eigenstates of physical Hamiltonians in a variational and targeted manner. This is…

Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the…

Many problems in physical chemistry involve systems that are coupled to an environment, such as a molecule interacting with an adjacent surface, possibly resulting in meta-stable molecular states where electron density is transferred to the…

We present a method to linearize, without approximation, a specific class of eigenvalue problems with eigenvector nonlinearities (NEPv), where the nonlinearities are expressed by scalar functions that are defined by a quotient of linear…

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…

We propose a novel adaptive damping algorithm for the self-consistent field (SCF) iterations of Kohn-Sham density-functional theory, using a backtracking line search to automatically adjust the damping in each SCF step. This line search is…

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…

Starting from a comparison of some established numerical algorithms for the computation of the eigenvalues (discrete or solitonic spectrum) of the non-Hermitian version of the Zakharov-Shabat spectral problem, this article delivers new…

We present a variational algorithm for fault tolerant quantum computing to solve a system of linear equations which directly maximises the parameters of the target fidelity. This so-called measurement test algorithm can be applied to any…

We present an efficient, fast and robust Nonlinear Fourier Transform (NFT) algorithm to detect eigenvalues of the discrete spectrum. It outperforms other known NFT algorithms as it detects the eigenvalues from the continuous spectrum, the…

In this paper, we propose efficient quantum algorithms for solving nonlinear stochastic differential equations (SDE) via the associated Fokker-Planck equation (FPE). We discretize the FPE in space and time using two well-known numerical…

We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…

This work studies the problem of maximizing a higher degree real homogeneous multivariate polynomial over the unit sphere. This problem is equivalent to finding the leading eigenvalue of the associated symmetric tensor of higher order,…

Nonlinear partial differential equations (PDEs) are crucial for modeling complex fluid dynamics and are foundational to many computational fluid dynamics (CFD) applications. However, solving these nonlinear PDEs is challenging due to the…