arXiv subjects

Hongfei Zhan

Publications and source records attributed to Hongfei Zhan.

4 recordsLinked to original sources

arXiv2026

An $h$-adaptive Tetrahedral Spectral Element Method with Applications to Kohn-Sham Density Functional Theory

High-order $h$-adaptive spectral element methods on tetrahedral meshes provide an effective framework for resolving localized singularities and multiscale structures in complex three-dimensional geometries. However, their development is often hindered by difficulties in maintaining $C^0$ continuity across refinement interfaces and efficiently transferring solutions between adaptive meshes. Such limitations are particularly relevant in demanding applications such as all-electron Kohn-Sham density functional theory, which place stringent requirements on the accurate resolution of both nuclear singularities and multiple physical scales. In this paper, we present an efficient $h$-adaptive tetrahedral spectral element framework. To address the continuity challenge, we develop an adaptive strategy that combines element orientation alignment with geometric red-green refinement, thereby eliminating the need for algebraic hanging-node constraints while preserving inter-element continuity. Furthermore, an efficient topology-based point-location algorithm is introduced to accelerate interpolation between adaptive meshes. Numerical experiments on Poisson and Laplacian eigenvalue problems confirm the spectral convergence of the proposed method. Applications to all-electron Kohn-Sham equations further demonstrate its capability to accurately resolve nuclear singularities. Moreover, parallel performance studies exhibit excellent scalability, with matrix assembly and adaptivity modules generally achieving speedups above 15 times and the proposed interpolation algorithm attaining speedups ranging from 25 to 35 on 64-core configurations compared to the single-core performance. These results indicate that the proposed framework provides an accurate, robust, and efficient solution for large-scale, high-resolution simulations.

math.NA↗

arXiv2025

Reducing Spatial and Temporal Dimensionality in the Multidimensional Caldeira-Leggett Model

Focusing on the real-time dynamics of the reduced density matrix of the multidimensional Caldeira-Leggett model, several techniques are adopted in this paper to reduce the spatial and temporal dimensionality, combined into an efficient algorithm. From a spatial perspective, an equivalent formulation of the Dyson series is presented. With the aid of a low-rank approximation, the spatial dimensionality of open quantum system simulations is halved. From a temporal perspective, the frozen Gaussian approximation is used to approximate both the evolution operator and the interaction operator in the multidimensional Caldeira-Leggett model. This reduces the high-dimensional integrals to one- and two-dimensional integrals independent of the truncation level of the Dyson series. Through these techniques, we design an efficient algorithm whose validity is verified through several numerical experiments, including a two-dimensional double slit simulation.

quant-ph↗

arXiv2024

A gradient flow model for ground state calculations in Wigner formalism based on density functional theory

In this paper, a gradient flow model is proposed for conducting ground state calculations in Wigner formalism of many-body system in the framework of density functional theory. More specifically, an energy functional for the ground state in Wigner formalism is proposed to provide a new perspective for ground state calculations of the Wigner function. Employing density functional theory, a gradient flow model is designed based on the energy functional to obtain the ground state Wigner function representing the whole many-body system. Subsequently, an efficient algorithm is developed using the operator splitting method and the Fourier spectral collocation method, whose numerical complexity of single iteration is $O(n_{\rm DoF}\log n_{\rm DoF})$. Numerical experiments demonstrate the anticipated accuracy, encompassing the one-dimensional system with up to $2^{21}$ particles and the three-dimensional system with defect, showcasing the potential of our approach to large-scale simulations and computations of systems with defect.

physics.comp-ph↗

arXiv2021

The Wigner Function of Ground State and One-Dimensional Numerics

In this paper, the ground state Wigner function of a many-body system is explored theoretically and numerically. First, an eigenvalue problem for Wigner function is derived based on the energy operator of the system. The validity of finding the ground state through solving this eigenvalue problem is obtained by building a correspondence between its solution and the solution of stationary Schrödinger equation. Then, a numerical method is designed for solving proposed eigenvalue problem in one dimensional case, which can be briefly described by i) a simplified model is derived based on a quantum hydrodynamic model [Z. Cai et al, J. Math. Chem., 2013] to reduce the dimension of the problem, ii) an imaginary time propagation method is designed for solving the model, and numerical techniques such as solution reconstruction are proposed for the feasibility of the method. Results of several numerical experiments verify our method, in which the potential application of the method for large scale system is demonstrated by examples with density functional theory.

quant-ph↗