Implicit Update Scheme for MPM The main purpose of this article is to talk about how to apply implicit update in MPM framework. To know more details about MPM, you can read This SIGGRAPH 2016 Course Notes and A Material Point Method For Snow Simulation (Alexey Stomakhin et al., 2013) . Framework of MPM Currently, I prefer to use APIC scheme to transfer velocity between particles and grids. The framework I always use is listed here:

Conjugate Gradient Method in Solving Linear Equation System Linear Equation System In fluid simulation, sometimes we need to solve a Linear Equation System like doing projection in Eulerian fluid. A linear Equation System can be written as a matrix form: $$ Ax = b $$ where $A$ is a $N\times N$ matrix and $x,b$ are $N\times 1$ vectors. Actually, we have a lot of methods to solve this problem, like Gauss-Seidel iteration, Gaussian elimination, etc.

Finite Elements Method for Simulating Elastic Body What do we do in simulating spring-mass system? Recall what we did in simulating Spring-Mass system: Firstly, we describe deformation of springs using $\mathbf{F} = \frac{\mathbf{x}_1 - \mathbf{x}_2}{l_0}$. Something noticable here is that $\mathbf{F}$ is a vector and it is related to rotation of springs. Then, we define strain $G = |\mathbf{F}| - 1$. The purpose of $G$ is that it is a scale and only related to stretch and contraction of springs.

A Start of this Website As a student major in Computer Science, I think it’s really cool to build my own website. In the past, I wrote some blogs in 洛谷. But the blog function has been cancled in 洛谷 now, so I am unable to design the webpage and you can only read the articles in column format(By the way, they’re all written in Chinese). In purpose of recording my feelings and displaying my CV and information like a researcher, I dicide to build this website with help of Hugo.