Related papers: Real-Space Adaptive-Coordinate Electronic Structur…
To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional…
For simulation studies of (macro) molecular liquids it would be of significant interest to be able to adjust or increase the level of resolution within one region of space, while allowing for the free exchange of molecules between open…
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…
Complex soft matter systems can be efficiently studied with the help of adaptive resolution simulation methods, concurrently employing two levels of resolution in different regions of the simulation domain. The non-matching properties of…
Fast and accurate measurement is a highly desirable, if not vital, feature of quantum computing architectures. In this work we investigate the usefulness of adaptive measurements in improving the speed and accuracy of qubit measurement. We…
Density functional theory (DFT) has emerged as one of the most versatile and lucrative approaches in electronic structure calculations of many-electron systems in past four decades. Here we give an account of the development of a…
We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of…
Recent advances in quantum computing and their increased availability has led to a growing interest in possible applications. Among those is the solution of partial differential equations (PDEs) for, e.g., material or flow simulation.…
In this paper, we consider the classical wave equation with time-dependent, spatially multiscale coefficients. We propose a fully discrete computational multiscale method in the spirit of the localized orthogonal decomposition in space with…
We have carried out numerical simulations of strongly gravitating systems based on the Einstein equations coupled to the relativistic hydrodynamic equations using adaptive mesh refinement (AMR) techniques. We show AMR simulations of NS…
We propose an adaptive quantum algorithm to prepare accurate variational time evolved wave functions. The method is based on the projected Variational Quantum Dynamics (pVQD) algorithm, that performs a global optimization with linear…
We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous $L^\infty$ coefficients. The methods are of Galerkin type and follow the…
The gas of the interacted electrons is usually described within Kohn-Sham approximation by the set of Poisson and Schr\"{o}dinger equations with an effective potential for the single-particle wave functions. The solution of these equations…
We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…
We have developed and implemented a new quantum molecular dynamics approximation that allows fast and accurate simulations of dense plasmas from cold to hot conditions. The method is based on a carefully designed orbital-free implementation…
We present a new multi-fluid, multi-temperature plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (non-linear, implicit) scheme for collisional low-temperature plasma. The particle transport is described using the…
In this paper, we study an adaptive finite element method for multiple eigenvalue problems of a class of second order elliptic equations. By using some eigenspace approximation technology and its crucial property which is also presented in…
In this paper, we introduce a highly accurate and efficient numerical solver for the radial Kohn--Sham equation. The equation is discretized using a high-order finite element method, with its performance further improved by incorporating a…
Accurate modeling of the electronic structure of warm dense matter is a challenging problem whose solution would allow a better understanding of material properties like equation of state, opacity, and conductivity, with resulting…
Boson is one of the most basic types of particles and preserves the commutation relation. An efficient way to measure a bosonic system is important not only for simulating complex physics phenomena of bosons (such as nuclei) on a qubit…