Related papers: Acceleration Schemes for Ab-Initio Molecular Dynam…
In ab initio molecular dynamics simulations of real-world problems, the simple Verlet method is still widely used for integrating the equations of motion, while more efficient algorithms are routinely used in classical molecular dynamics.…
We push the boundaries of electronic structure-based \textit{ab-initio} molecular dynamics (AIMD) beyond 100 million atoms. This scale is otherwise barely reachable with classical force-field methods or novel neural network and machine…
We develop convergence acceleration procedures that enable a gradient descent-type iteration method to efficiently simulate Hartree--Fock equations for atoms interacting both with each other and with an external potential. Our development…
In this paper, we consider numerical approximations for the viscous Cahn-Hilliard equation with hyperbolic relaxation. This type of equations processes energy-dissipative structure. The main challenge in solving such a diffusive system…
In this work we present an a priori error analysis for solving the unsteady advection equation on cut cell meshes along a straight ramp in two dimensions. The space discretization uses a lowest order upwind-type discontinuous Galerkin…
Optimization in machine learning, both theoretical and applied, is presently dominated by first-order gradient methods such as stochastic gradient descent. Second-order optimization methods, that involve second derivatives and/or second…
We extend the static theory of disorder-induced exponential decay of the averaged Green function of a quantum charged particle in a classical one-component plasma to the dynamic regime by incorporating the temporal evolution of the ionic…
Structure-preserving numerical schemes for a nonlinear parabolic fourth-order equation, modeling the electron transport in quantum semiconductors, with periodic boundary conditions are analyzed. First, a two-step backward differentiation…
Semi-discrete Galerkin formulations of transient wave equations, either with conforming or discontinuous Galerkin finite element discretizations, typically lead to large systems of ordinary differential equations. When explicit time…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
A quasi-second order scheme is developed to obtain approximate solutions of the shallow water equationswith bathymetry. The scheme is based on a staggered finite volume scheme for the space discretization:the scalar unknowns are located in…
In this work, we analyze Parametrized Advection-Dominated distributed Optimal Control Problems with random inputs in a Reduced Order Model (ROM) context. All the simulations are initially based on a finite element method (FEM)…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
In this work, we consider a system of two wave equations coupled by velocities in one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling…
Computer simulation methods, such as Monte Carlo or Molecular Dynamics, are very powerful computational techniques that provide detailed and essentially exact information on classical many-body problems. With the advent of ab-initio…
Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…
We propose, analyze mathematically, and study numerically a novel approach for the finite element approximation of the spectrum of second-order elliptic operators. The main idea is to reduce the stiffness of the problem by subtracting a…
An adpative integration technique for time advancement of particle motion in the context of coupled computational fluid dynamics (CFD) - discrete element method (DEM) simulations is presented in this work. CFD-DEM models provide an accurate…
We show that optimal control of the electron dynamics is able to prepare molecular ground states, within chemical accuracy, with evolution times approaching the bounds imposed by quantum mechanics. We propose a specific parameterization of…
We present and analyze two stabilized finite element methods for solving numerically the Poisson--Nernst--Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for…