Related papers: Real-Space Mesh Techniques in Density Functional T…
A recently proposed linear-scaling scheme for density-functional pseudopotential calculations is described in detail. The method is based on a formulation of density functional theory in which the ground state energy is determined by…
Multidimensional systems are becoming increasingly important as they provide a promising tool for estimation, simulation and control, while going beyond the traditional setting of one-dimensional systems. The analysis of multidimensional…
We present a real-space formulation for isotropic Fourier-space preconditioners used to accelerate the self-consistent field iteration in Density Functional Theory calculations. Specifically, after approximating the preconditioner in…
We present details of our effective computational methods based on the real-space finite-difference formalism to elucidate electronic and magnetic properties of the two-dimensional (2D) materials within the framework of the density…
We present a novel differentiable grid-based representation for efficiently solving differential equations (DEs). Widely used architectures for neural solvers, such as sinusoidal neural networks, are coordinate-based MLPs that are both…
Density matrix embedding theory (DMET) is a fully quantum-mechanical embedding method which shows great promise as a method of defeating the inherent exponential cost scaling of multiconfigurational wave function-based calculations by…
Large-scale applications of energy density functional (EDF) methods depend on fast and reliable algorithms to solve the associated non-linear self-consistency problem. When dealing with large single-particle variational spaces, existing…
In this paper, we present a sparse grid-based Monte Carlo method for solving high-dimensional semi-linear nonlocal diffusion equations with volume constraints. The nonlocal model is governed by a class of semi-linear partial…
Physically-motivated and mathematically robust atom-centred representations of molecular structures are key to the success of modern atomistic machine learning (ML) methods. They lie at the foundation of a wide range of methods to predict…
A numerical framework is developed to solve various types of PDEs on complicated domains, including steady and time-dependent, non-linear and non-local PDEs, with different boundary conditions that can also include non-linear and non-local…
Neural implicit representations, including Neural Distance Fields and Neural Radiance Fields, have demonstrated significant capabilities for reconstructing surfaces with complicated geometry and topology, and generating novel views of a…
Chemical accuracy serves as an important metric for assessing the effectiveness of the numerical method in Kohn--Sham density functional theory. It is found that to achieve chemical accuracy, not only the Kohn--Sham wavefunctions but also…
Atomic-resolution imaging with scanning transmission electron microscopy is a powerful tool for characterizing the nanoscale structure of materials, in particular features such as defects, local strains, and symmetry-breaking distortions.…
We present a real-space formulation for coarse-graining Kohn-Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps.…
The purpose of this paper is to analyze a mixed method for linear elasticity eigenvalue problem, which approximates numerically the stress, displacement, and rotation, by piecewise $(k+1)$, $k$ and $(k+1)$-th degree polynomial functions…
We present an implementation in a linear-scaling density-functional theory code of an electronic enthalpy method, which has been found to be natural and efficient for the ab initio calculation of finite systems under hydrostatic pressure.…
We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on solvers…
In the present chapter we focus on the fundamentals of non-grid-conforming numerical approaches to simulating particulate flows, implementation issues and grid convergence vs. available reference data. The main idea is to avoid adapting the…
In modeling low-dimensional electronic nanostructures, the evaluation of the electron-electron interaction is a challenging task. Here we present an accurate and practical density-functional approach to the two-dimensional many-electron…
We present an accurate and efficient formulation of the stress tensor for real-space Kohn-Sham Density Functional Theory (DFT) calculations. Specifically, while employing a local formulation of the electrostatics, we derive a linear-scaling…