196 citations · 1.6k across the 143 of their papers we have counts for
8 papers · 2 filters
Numerical methods for stochastic differential equations based on Gaussian mixture
Lei Li, Jianfeng Lu, Jonathan Mattingly +1
We develop in this work a numerical method for stochastic differential equations (SDEs) with weak second order accuracy based on Gaussian mixture. Unlike the conventional higher or…
A Numerical method for coupling the BGK model and Euler equation through the linearized Knudsen layer
Hongxu Chen, Qin Li, Jianfeng Lu
The Bhatnagar-Gross-Krook (BGK) model, a simplification of the Boltzmann equation, in the absence of boundary effect, converges to the Euler equations when the Knudsen number is sm…
Random Sampling and Efficient Algorithms for Multiscale PDEs
Ke Chen, Qin Li, Jianfeng Lu +1
We describe a numerical framework that uses random sampling to efficiently capture low-rank local solution spaces of multiscale PDE problems arising in domain decomposition. In con…
Integrated Tempering Enhanced Sampling Method as the Infinite Switching Limit of Simulated Tempering
Zhiyi You, Liying Li, Jianfeng Lu +1
Fast and accurate sampling method is in high demand, in order to bridge the large gaps between molecular dynamic simulations and experimental observations. Recently, integrated tem…
Coordinate-wise descent methods for leading eigenvalue problem
Yingzhou Li, Jianfeng Lu, Zhe Wang
Leading eigenvalue problems for large scale matrices arise in many applications. Coordinate-wise descent methods are considered in this work for such problems based on a reformulat…
Quadrature Points via Heat Kernel Repulsion
Jianfeng Lu, Matthias Sachs, Stefan Steinerberger
We discuss the classical problem of how to pick weighted points on a dimensional manifold so as to obtain a reasonable quadrature rule $$ \frac{1}{|M|}\int_{M}{f(x) dx} \si…
Optimal artificial boundary condition for random elliptic media
Jianfeng Lu, Felix Otto
We are given a uniformly elliptic coefficient field that we regard as a realization of a stationary and finite-range (say, range unity) ensemble of coefficient fields. Given a (det…
Stochastic dynamical low-rank approximation method
Yu Cao, Jianfeng Lu
In this paper, we extend the dynamical low-rank approximation method to the space of finite signed measures. Under this framework, we derive stochastic low-rank dynamics for stocha…