相关论文: Real-Space Adaptive-Coordinate Electronic Structur…
We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule…
We present a multigrid algorithm for the solution of the linear systems of equations stemming from the $p-$version of the Virtual Element discretization of a two-dimensional Poisson problem. The sequence of coarse spaces are constructed…
Using a novel self-consistent implementation of Hedin's GW perturbation theory we calculate space and energy dependent self-energy for a number of materials. We find it to be local in real space and rapidly convergent on second-- to third--…
A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the…
A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the…
Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by…
Molecular dynamics simulations are indispensable for exploring the behavior of atoms and molecules. Grounded in quantum mechanical principles, quantum molecular dynamics provides high predictive power but its computational cost is dominated…
We propose a collocation method based on multivariate polynomial splines over triangulation or tetrahedralization for the numerical solution of partial differential equations. We start with a detailed explanation of the method for the…
We describe a grid-based numerical method for 3D hydrodynamic cosmological simulations which is adaptive in space and time and combines the best features of higher order--accurate Godunov schemes for Eulerian hydrodynamics with adaptive…
Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report…
By applying the projector to the filled lattice eigenstates on a specific position, or applying the local electron annihilation operator on the many-body ground state, one can construct a quantum state localized around a specific position…
A parallel, relativistic, three-dimensional particle-in-cell code SPACE has been developed for the simulation of electromagnetic fields, relativistic particle beams, and plasmas. In addition to the standard second-order Particle-in-Cell…
For the numerical simulations of physical and mechanical behaviors of materials at the micro-nano scale, a coupled model with the effect of local quantum is presented in this paper. Unlike traditional methods, the transition region is not…
Quantum harmonic oscillators, or qumodes, provide a promising and versatile framework for quantum computing. Unlike qubits, which are limited to two discrete levels, qumodes have an infinite-dimensional Hilbert space, making them…
We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The…
We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of…
In this paper we present an adaptive discretization technique for solving elliptic partial differential equations via a collocation radial basis function partition of unity method. In particular, we propose a new adaptive scheme based on…
The present article investigates the convergence of a class of space-time discretization schemes for the Cauchy problem for linear parabolic stochastic partial differential equations (SPDEs) defined on the whole space. Sufficient conditions…
A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid…
Modeling composite systems of spins or electrons coupled to bosonic modes is of significant interest for many fields of applied quantum physics and chemistry. A quantum simulation can allow for the solution of quantum problems beyond…