Code Fields

Software

This part are self-contained and mature packages.

DGESMAT [Github]

DGESMAT is a MATLAB toolbox designed for calculating Electronic Structure eigenvalue problems within the Discontinuous Galerkin (DG) framework based on the Kohn-Sham density functional theory (DFT). The flexibility of the DG framework has two significant impacts. Firstly, it allows the utilization of discontinuous basis functions to approximate the continuous Kohn-Sham orbitals, enabling high accuracy in total energy calculations with a small number of basis functions per atom. Secondly, it exhibits high parallel efficiency through a multi-level parallelization scheme, which is beneficial for practical implementations.

DGESMAT aims to simplify the prototyping and testing of new algorithms for solving the Kohn-Sham problem within the DG framework. It achieves this by utilizing MATLAB’s parfor to handle part of the parallelization, eliminating the need for complex MPI programming. Additionally, DGESMAT leverages MATLAB’s object-oriented features and operator overloading to represent wavefunctions, Hamiltonians, and their operations, making it beginner-friendly for individuals new to this field.

Currently, DGESMAT employs standard pseudopotentials and supports local density approximation (LDA), generalized gradient approximation (GGA), and hybrid functionals. Furthermore, future releases will incorporate time-dependent DFT and post-DFT calculations to expand its capabilities.

AI Product

This part are some codes relatived to LLM and AI.

Referee Response Harness [Github]

A Codex skill that helps you setup the auxiliary files used for a LaTeX paper revision—from reviewer comments to an author-approved response. It creates and maintains a self-contained revision harness adapted to each paper’s sources, reviewer reports, deliverables, and workflow.

The general workflow used in this harness is

• The agent first extracts concerns of referees and proposes clusters from their dependencies.

• Follow the cluster sequence to discuss concerns and possible treatments with the agent.

• Ask the agent to complete the revision of each cluster and generate diff files.

• The consistency check is usually used after the author do some manual edition.

• The agent writes the response letter based on the revised paper.

Code

This part are some independent codes for particular usage.

FGAFSE [Github]

FGAFSE is a MATLAB code that offers an implementation of the Frozen Gaussian Approximation (FGA) solver for the fractional Schrödinger equation (FSE) in the semi-classical regime. In this regime, the solution exhibits high oscillations when the scaled Planck constant $\varepsilon$ is small. The FGA method provides an efficient computational approach by approximating the solution to the Schrödinger equation using an integral representation derived from asymptotic analysis. It offers a highly accurate and efficient method for the evolution of high-frequency wave functions. We also provide numerical examples in both one and two dimensions to demonstrate the accuracy and effectiveness of the FGA method by comparing it with the Time Splitting Spectral Approximation method.

Tex2docx [Github]

This is a guide of using “Pandoc+Panflute” to convert LaTeX file to Docx format. While Pandoc can convert LaTeX to Docx, the conversion is not always be perfect, as the two formats have different capabilities and features. Manual adjustments or fine-tuning may be required after the conversion, to ensure the document appears as intended in the new format. The goal of this project is to showcase the workflow of customized Pandoc, a tailored version of Pandoc that aims to minimize the need for manual adjustments.

SinCoTrap [Github]

SinCoTrap (Singularity-Corrected Trapezoidal Rule) is a high-order locally corrected trapezoidal method for periodic singular integrals. It targets kernels of the form $|\boldsymbol{x}|^{-s}$ with $0 < s < d$, while preserving the uniform tensor grid and modifying only a small fixed stencil of weights near the singularity. Specifically, we focus on singular integrals in arbitrary dimension $d$ that takes the form

\[I[\varphi \cdot \sigma] = \int_{[-a, a]^d} \varphi(\boldsymbol{x}) \sigma(\boldsymbol{x}) \mathrm{d} \boldsymbol{x}, \quad \sigma(\boldsymbol{x}) = \frac{1}{|\boldsymbol{x}|^{s}}, \quad \boldsymbol{x} \in \mathbb{R}^d. \nonumber\]

Equivalently, $\varphi\cdot\sigma$ defines a $C^{\infty}$ function on the punctured torus.

For correction order $p$, the corrected quadrature achieves the error rate $O(h^{2p+2+d-s})$. The correction weights are mesh-independent and they can be precomputed via analytic continuation of a special generalization of the Riemann zeta function for a given $(d, s, p)$. This makes SinCoTrap both efficient in application and robust for high-order accuracy across a broad class of periodic singular integrals.