Related papers: A reduced scalar potential approach for magnetosta…
Modeling contact mechanics with high contrast coefficients presents significant mathematical and computational challenges, especially in achieving strongly symmetric stress approximations for mixed formulations. Due to the inherent…
We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo…
We describe stochastic Newton and stochastic quasi-Newton approaches to efficiently solve large linear least-squares problems where the very large data sets present a significant computational burden (e.g., the size may exceed computer…
The computational cost associated with reducing tensor integrals to scalar integrals using the Passarino-Veltman method is dominated by the diagonalisation of large systems of equations. These systems of equations are sized according to the…
The Petviashvili's iteration method has been known as a rapidly converging numerical algorithm for obtaining fundamental solitary wave solutions of stationary scalar nonlinear wave equations with power-law nonlinearity: \ $-Mu+u^p=0$, where…
Highly flexible Jastrow factors have found significant use in stochastic electronic structure methods such as variational Monte Carlo (VMC) and diffusion Monte Carlo, as well as in quantum chemical transcorrelated (TC) approaches, which…
This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…
We focus on finding sparse and least-$\ell_1$-norm solutions for unconstrained nonlinear optimal control problems. Such optimization problems are non-convex and non-smooth, nevertheless recent versions of Newton method for under-determined…
We describe a three precision variant of Newton's method for nonlinear equations. We evaluate the nonlinear residual in double precision, store the Jacobian matrix in single precision, and solve the equation for the Newton step with…
This paper describes a new Monte Carlo method based on a novel stochastic potential switching algorithm. This algorithm enables the equilibrium properties of a system with potential $V$ to be computed using a Monte Carlo simulation for a…
The recently introduced scheme [20,21] is extended to propose an algebraic non-perturbative approach for the analytical treatment of Schr\"odinger equations with non-solvable potentials involving an exactly solvable potential form together…
A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
The classical method to solve a quadratic optimization problem with nonlinear equality constraints is to solve the Karush-Kuhn-Tucker (KKT) optimality conditions using Newton's method. This approach however is usually computationally…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
Slater determinants have underpinned quantum chemistry for nearly a century, yet their full potential has remained challenging to exploit. In this work, we show that a variational wavefunction composed of a few hundred optimized…
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 document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
In this paper, nonlinear model reduction for power systems is performed by the balancing of empirical controllability and observability covariances that are calculated around the operating region. Unlike existing model reduction methods,…
This paper presents a novel methodology for evaluating the boundedness, stability, and instability of some vector nonlinear systems with multiple time-varying delays and variable coefficients. The proposed technique develops two scalar…