Related papers: Stabilization of Ab Initio Molecular Dynamics Simu…
Available simulation methods, suitable to describe solid-solid phase transitions occurring upon increasing of presssure and/or temperature, are based on empirical interatomic potentials: this restriction reduces the predictive power, and…
Multiphase flow in porous media occurs in several disciplines including petroleum reservoir engineering, petroleum systems' analysis, and CO$_2$ sequestration. While simulations often use a fully implicit discretization to increase the time…
We introduce an efficient scheme for the molecular dynamics of electronic systems by means of quantum Monte Carlo. The evaluation of the (Born-Oppenheimer) forces acting on the ionic positions is achieved by two main ingredients: i) the…
Multiple time scale molecular dynamics enhances computational efficiency by updating slow motions less frequently than fast motions. However, in practice the largest outer time step possible is limited not by the physical forces but by…
A new model for the numerical simulation of a rigid body moving in a viscous fluid flow using FEM is presented. One of the most interesting features of this approach is the small computational effort required to solve the motion of the…
The vortex-induced vibration of multiple spring-mounted bodies free to move in the orthogonal direction of the flow is investigated. In a first step, we derive a Linear Arbitrary Lagrangian Eulerian (L-ALE) method to solve the…
The phenomenon of solidification of a substance from its liquid phase is of the greatest practical and theoretical importance, and atomistic simulations can provide precious information towards its understanding and control. Unfortunately,…
We have developed an efficient and unconditionally energy-stable method for simulating droplet formation dynamics. Our approach involves a novel time-marching scheme based on the scalar auxiliary variable technique, specifically designed…
The finite element method is one of the widely employed numerical techniques in electrical engineering for the study of electric and magnetic fields. When applied to the moving conductor problems, the finite element method is known to have…
The behavior of an atom in a molecule, liquid or solid is governed by the force it experiences. If the dependence of this vectorial force on the atomic chemical environment can be $learned$ efficiently with high-fidelity from benchmark…
We present a simulation scheme for discrete-velocity gases based on {\em local thermodynamic equilibrium}. Exploiting the kinetic nature of discrete-velocity gases, in that context, results in a natural splitting of fluxes, and the…
In this work, we explore various relevant aspects of the Smoothed Particle Hydrodynamics regarding Burger's equation. The stability, precision, and efficiency of the algorithm are investigated in terms of different implementations. In…
We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis…
The design of microfluidic devices is a cumbersome and tedious process that can be significantly improved by simulation. Methods based on Computational Fluid Dynamics (CFD) are considered state-of-the-art, but require extensive compute time…
For over three decades, the front-capturing level-set method has demonstrated its prowess for the simulation, at the mesoscopic scale, of numerous mechanisms in the context of microstructure evolution occurring during complex…
The Biot-Savart law is relevant in physical contexts including electromagnetism and fluid dynamics. In the latter case, when the rotation of a fluid is confined to a set of very thin vortex filaments, this law describes the velocity field…
Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed…
The leapfrog integrator is widely used because of its excellent stability in molecular dynamics simulation. This is recognized as being due to the existence of a discrete variational structure of the equations. We introduce a modified…
We discretize the Lagrange multiplier formulation of the obstacle problem by mixed and stabilized finite element methods. A priori and a posteriori error estimates are derived and numerically verified.
We analyse the Virtual Element Methods (VEM) on a simple elliptic model problem, allowing for more general meshes than the one typically considered in the VEM literature. For instance, meshes with arbitrarily small edges (with respect to…