Related papers: Solvers for Large-Scale Electronic Structure Theor…

Vertex Subset Problems (VSPs) are a class of combinatorial optimization problems on graphs where the goal is to find a subset of vertices satisfying a predefined condition. Two prominent approaches for solving VSPs are dynamic programming…

In this work we present RESCU, a powerful MATLAB-based Kohn-Sham density functional theory (KS-DFT) solver. We demonstrate that RESCU can compute the electronic structure properties of systems comprising many thousands of atoms using modest…

Solving large-scale sparse linear systems is a challenging computational task due to the introduction of non-zero elements, or "fill-in." The Graph Partitioning Problem (GPP) arises naturally when minimizing fill-in and accelerating…

Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields, ranging from materials science to biochemistry to…

Simulating diffusion in heterogeneous media presents a significant computational challenge, as resolving microscopic physical scales traditionally demands excessively fine computational grids. To overcome this barrier, we extend the…

Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. An efficient algorithm for the…

Modern very large-scale integration (VLSI) design requires the implementation of integrated circuits using electronic design automation (EDA) tools. Due to the complexity of EDA algorithms, the vast parameter space poses a huge challenge to…

We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To…

In a recent article [1], the FEAST algorithm has been presented as a general purpose eigenvalue solver which is ideally suited for addressing the numerical challenges in electronic structure calculations. Here, FEAST is presented beyond the…

Unlike the local density approximation (LDA) and the generalized gradient approximation (GGA), calculations with meta-generalized gradient approximations (meta-GGA) are usually done according to the generalized Kohn-Sham (gKS) formalism.…

Large language models (LLMs) are increasingly used for generating parallel scientific codes, with a primary focus on generating functionally correct code. Recent work has focused on generating performant code, with an emphasis on its…

Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method…

Reducing parameter spaces via exploiting symmetries has greatly accelerated and increased the quality of electronic-structure calculations. Unfortunately, many of the traditional methods fail when the global crystal symmetry is broken, even…

An exchange-correlation energy functional beyond the local density approximation, based on the exchange-correlation kernel of the homogeneous electron gas and originally introduced by Kohn and Sham, is considered for electronic structure…

Large Language Models (LLMs) have demonstrated remarkable performance across a wide range of tasks, but their deployment is often constrained by substantial memory footprints and computational costs. While prior work has achieved…

Overfitting and treatment of "small data" are among the most challenging problems in the machine learning (ML), when a relatively small data statistics size $T$ is not enough to provide a robust ML fit for a relatively large data feature…

Iterative multiscale methods for electronic structure calculations offer several advantages for large-scale problems. Here we examine a nonlinear full approximation scheme (FAS) multigrid method for solving fixed potential and…

First-principles electronic structure calculations are very widely used thanks to the many successful software packages available. Their traditional coding paradigm is monolithic, i.e., regardless of how modular its internal structure may…

Accurate first-principles calculations for the energies, charge distributions, and spin symmetries of many-electron systems are essential to understand and predict the electronic and structural properties of molecules and materials.…

We derive a self-consistent local variant of the Thomas-Fermi approximation for (quasi-)two-dimensional (2D) systems by localizing the Hartree term. The scheme results in an explicit orbital-free representation of the electron density and…