## Crouzeix’s divergence free basis for the Navier-Stokes equation

This is the solution (long read) to a Chapter 11 exercise of the book by Brenner and Scott (Brenner and Scott, 2008). Personally I really like this problem, ...

This is the solution (long read) to a Chapter 11 exercise of the book by Brenner and Scott (Brenner and Scott, 2008). Personally I really like this problem, ...

In the first part, we reviewed a brief history of the mathematics of the Quantum Field Theory (not exhaustively, but enough to get the idea). In this part, w...

Translating the language of physicists to the language of mathematicians.

This note walks through the construction of the stiffness matrix for the finite element approximation of Poisson equation in 2D using the hierarchical basis...

My experience of using the GitHub copilot as a computational mathematician.

Use VSCode task to streamline the workflow of building a site and push the changes to GitHub.

Install wgo.js in the Jekyll blog and load it on demand using a toggle in preamble.

GitHub pages allows Jekyll version only to be 3.9, let us find a way around it.

A newbie’s journey of submitting his first ML paper to a top conference.

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

Configuring Ubuntu to use integrated graphics for display and CUDA for computing, best for a single-GPU setup.

Assembling of a deep learning workstation with RTX 3090 + 10850k, and how to deal with the bent of the heavy 3090 card.

A random newbie’s story on building an RTX 3090 workstation.

How to write elegantly fast code to handle cell array with different length vector at each row.

This notes contains some of the notes I used in UC Irvine Math 130C course.

I finally decided to migrate various of my old writing in my faculty website at UC Irvine (deactivated as of Oct 2020) a static website generator Jekyll. App...

Some detective work on the trace lemmata (and the converse one) for the Sobolev spaces.

Matlab finally embraces (partially) the way matrix manipulation should be Starting in MATLAB R2016b with the addition of implicit expansion, some combinatio...

本文前半部分是介绍Kaggle的机器学习比赛，后半则是记录今年3月到6月带领几位University of California, Irvine数学系本科生参加由美国洛斯阿拉莫斯国家实验室在Kaggle上组织的地震预测比赛。

In the course project, groups of three students will work together to create regression/classifiers for an in-class Kaggle prediction competition. The compet...

I created an introductory machine learning class for math undergrad who has no previous exposure to programming back in Winter 2019 quarter. This post will t...

这个简明教程主要是教大家使用强大的LaTeX宏包TikZ来绘制工作生活中需要的一些示意图。

Using Poincare lemma to construct vector field explicitly for Helmholtz decomposition.

Since Google+ is finally to be shut down by Google as of Feb 1, 2019, aside from migrating G+’s social bookmarking functionality to Medium.com and Pocket app...

This short post explores the equivalence between Sobolev norm and Sobolev-Slobodeckij norm for $W^{s,p}(\Omega)$ when $s$ is an integer.

这是很久以前在果壳小组写的外行解读帖子，现在果壳小组没有了，把自己以前给果壳写的帖子留个备份。

This is a continuation of my previous “complaining” post on the language difference of mathematician vs physicists regarding the same thing.

I took a quantum physics class on Coursera this year and I found that the Mathematical language spoken by the two communities, math vs physics, are quite dif...

Here we present two approaches to construct Helmholtz decompositions.

This is an exercise in Evans, Partial Differential Equations (1st edition), page 164, problem 13.

This is a post recording my answer to a question on Math StackExchange1 with some references in L. Tartar’s book2. https://math.stackexchange...

This is an exercise for finite element method most likely. Our question is:

First about the appropriate boundary condition we would like to impose: The cross product(scalar-$\mathrm{curl}$) in $\mathbb{R}^2$ is done by we embed a vec...

Sobolev embedding When $p=n$

This is an exercise in Evans, Partial Differential Equations (2nd edition), Chapter 10 Conservation laws.

PDE This was the first project after I switched to a PhD program in computational math. The goal of the project is to study the Discontinuous Galerkin (DG) f...