Related papers: A New Time-Reversible Integrator for Molecular Dyn…
In recent decades, there have been many attempts to construct symplectic integrators with variable time steps, with rather disappointing results. In this paper we identify the causes for this lack of performance, and find that they fall…
Suitable discretizations through tensor product formulas of popular multidimensional operators (diffusion or diffusion--advection, for instance) lead to matrices with $d$-dimensional Kronecker sum structure. For evolutionary Partial…
This paper addresses the problem of efficiently computing higher-order variational integrators in simulation and trajectory optimization of mechanical systems as those often found in robotic applications. We develop $O(n)$ algorithms to…
We suggest a numerical integration procedure for solving the equations of motion of certain classical spin systems which preserves the underlying symplectic structure of the phase space. Such symplectic integrators have been successfully…
In this paper, we study a tensor-based method for the numerical solution of a class of diffusion--reaction equations defined on spatial domains that admit common curvilinear coordinate representations. Typical examples in 2D include disks…
The explicit split-operator algorithm has been extensively used for solving not only linear but also nonlinear time-dependent Schr\"{o}dinger equations. When applied to the nonlinear Gross-Pitaevskii equation, the method remains…
Molecular dynamics simulations are an important tool for describing the evolution of a chemical system with time. However, these simulations are inherently held back either by the prohibitive cost of accurate electronic structure theory…
We change a previous time-stepping algorithm for solving a multi-scale Vlasov-Poisson system within a Particle-In-Cell method, in order to do accurate long time simulations. As an exponential integrator, the new scheme allows to use large…
In this paper we continue our work on adaptive timestep control for weakly non- stationary problems. The core of the method is a space-time splitting of adjoint error representations for target functionals due to S\"uli and Hartmann. The…
We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed…
A common problem in physics and engineering is determination of the orientation of an object given its angular velocity. When the direction of the angular velocity changes in time, this is a nontrivial problem involving coupled differential…
The nonlinear, or warped, resolvent recently explored by Giselsson and B\`ui-Combettes has been used to model a large set of existing and new monotone inclusion algorithms. To establish convergent algorithms based on these resolvents,…
We investigate time-adaptive Magnus-type integrators for the numerical approximation of a Mott transistor. The rapidly attenuating electromagnetic field calls for adaptive choice of the time steps. As a basis for step selection,…
We present a new formulation of ab initio molecular dynamics which exploits the efficiency of plane waves in adaptive curvilinear coordinates, and thus provides an accurate treatment of first-row elements. The method is used to perform a…
In this paper, modulating functions-based method is proposed for estimating space-time dependent unknowns in one-dimensional partial differential equations. The proposed method simplified the problem into a system of algebraic equations…
A numerical integrator is presented that computes a symmetric or skew-symmetric low-rank approximation to large symmetric or skew-symmetric time-dependent matrices that are either given explicitly or are the unknown solution to a matrix…
Molecular dynamics simulation is used to investigate the crystallization of a classical two-dimensional electron system, in which electrons interact with the Coulomb repulsion. From the positional and the orientational correlation…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
Motivated by fractional derivative models in viscoelasticity, a class of semilinear stochastic Volterra integro-differential equations, and their deterministic counterparts, are considered. A generalized exponential Euler method, named here…
Data-Driven Computational Mechanics is a novel computing paradigm that enables the transition from standard data-starved approaches to modern data-rich approaches. At this early stage of development, one can distinguish two mainstream…