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Browsing by Author "Lu, J"
Now showing items 120 of 71

A convergent method for linear halfspace kinetic equations
Li, Q; Lu, J; Sun, W (20170423)We give a unified proof for the wellposedness of a class of linear halfspace equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main ... 
A Diabatic Surface Hopping Algorithm based on Time Dependent Perturbation Theory and Semiclassical Analysis
Fang, D; Lu, J (20171130)Surface hopping algorithms are popular tools to study dynamics of the quantumclassical mixed systems. In this paper, we propose a surface hopping algorithm in diabatic representations, based on time dependent perturbation ... 
A Mathematical Theory of Optimal Milestoning (with a Detour via Exact Milestoning)
Lin, L; Lu, J; VandenEijnden, E (20170423)Milestoning is a computational procedure that reduces the dynamics of complex systems to memoryless jumps between intermediates, or milestones, and only retains some information about the probability of these jumps and the ... 
A Quantum Kinetic Monte Carlo Method for Quantum Manybody Spin Dynamics
Cai, Z; Lu, J (20171130)We propose a general framework of quantum kinetic Monte Carlo algorithm, based on a stochastic representation of a series expansion of the quantum evolution. Two approaches have been developed in the context of quantum manybody ... 
A quasinonlocal coupling method for nonlocal and local diffusion models
Du, Q; Li, XH; Lu, J; Tian, X (20170423)In this paper, we extend the idea of "geometric reconstruction" to couple a nonlocal diffusion model directly with the classical local diffusion in one dimensional space. This new coupling framework removes interfacial ... 
A stochastic version of Stein Variational Gradient Descent for efficient sampling
Li, L; Li, Y; Liu, JG; Liu, Z; Lu, JWe propose in this work RBMSVGD, a stochastic version of Stein Variational Gradient Descent (SVGD) method for efficiently sampling from a given probability measure and thus useful for Bayesian inference. The method is to apply ... 
A Surface Hopping Gaussian Beam Method for HighDimensional Transport Systems
Cai, Z; Lu, J (20170423)We propose a surface hopping Gaussian beam method to numerically solve a class of high frequency linear transport systems in high spatial dimensions, based on asymptotic analysis. The stochastic surface hopping is combined ... 
A variational perspective on cloaking by anomalous localized resonance
Kohn, RV; Lu, J; Schweizer, B; Weinstein, MI (Communications in Mathematical Physics, 20140314)© SpringerVerlag Berlin Heidelberg 2014.A body of literature has developed concerning “cloaking by anomalous localized resonance.” The mathematical heart of the matter involves the behavior of a divergenceform elliptic ... 
Adaptive local basis set for KohnSham density functional theory in a discontinuous Galerkin framework I: Total energy calculation
Lin, L; Lu, J; Ying, L; E, W (Journal of Computational Physics, 20120220)KohnSham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the KohnSham Hamiltonian generally results in a large number ... 
An asymptotic preserving method for transport equations with oscillatory scattering coefficients
Li, Q; Lu, J (20170426)We design a numerical scheme for transport equations with oscillatory periodic scattering coefficients. The scheme is asymptotic preserving in the diffusion limit as Knudsen number goes to zero. It also captures ... 
Analysis of the divideandconquer method for electronic structure calculations
Chen, J; Lu, J (20170426)We study the accuracy of the divideandconquer method for electronic structure calculations. The analysis is conducted for a prototypical subdomain problem in the method. We prove that the pointwise difference between electron ... 
Analysis of time reversible bornoppenheimer molecular dynamics
Lin, L; Lu, J; Shao, S (Entropy, 20140101)We analyze the time reversible BornOppenheimer molecular dynamics (TRBOMD) scheme, which preserves the time reversibility of the BornOppenheimer molecular dynamics even with nonconvergent selfconsistent field iteration. ... 
Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model
Liu, JG; Lu, J; Margetis, D; Marzuola, JL (20170423)In the absence of external material deposition, crystal surfaces usually relax to become flat by decreasing their free energy. We study an asymmetry in the relaxation of macroscopic plateaus, facets, of a periodic surface ... 
ButterflyNet: Optimal Function Representation Based on Convolutional Neural Networks
Li, Y; Cheng, X; Lu, JDeep networks, especially Convolutional Neural Networks (CNNs), have been successfully applied in various areas of machine learning as well as to challenging problems in other scientific and engineering fields. ... 
Combining 2D synchrosqueezed wave packet transform with optimization for crystal image analysis
Lu, J; Wirth, B; Yang, H (Journal of the Mechanics and Physics of Solids, 20160401)© 2016 Elsevier Ltd. All rights reserved.We develop a variational optimization method for crystal analysis in atomic resolution images, which uses information from a 2D synchrosqueezed transform (SST) as input. ... 
Complexity of randomized algorithms for underdamped Langevin dynamics
Cao, Y; Lu, J; Wang, LWe establish an information complexity lower bound of randomized algorithms for simulating underdamped Langevin dynamics. More specifically, we prove that the worst $L^2$ strong error is of order $\Omega(\sqrt{d}\, N^{3/2})$, ... 
Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost
Lu, J; Ying, L (Journal of Computational Physics, 20151201)© 2015 Elsevier Inc.Electron repulsion integral tensor has ubiquitous applications in electronic structure computations. In this work, we propose an algorithm which compresses the electron repulsion tensor into the tensor ... 
Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces
Gao, Y; Liu, JG; Lu, J (Journal of Nonlinear Science, 20161229)This work considers the rigorous derivation of continuum models of step motion starting from a mesoscopic Burton–Cabrera–Franktype model following the Xiang’s work (Xiang in SIAM J Appl Math 63(1):241–258, 2002). We prove ... 
Convergence of a ForceBased Hybrid Method in Three Dimensions
Lu, J; Ming, P (Communications on Pure and Applied Mathematics, 20130101)We study a forcebased hybrid method that couples an atomistic model with the CauchyBorn elasticity model. We show that the proposed scheme converges to the solution of the atomistic model with secondorder accuracy, since ... 
Convergence of frozen Gaussian approximation for highfrequency wave propagation
Lu, J; Yang, X (Communications on Pure and Applied Mathematics, 20120601)The frozen Gaussian approximation provides a highly efficient computational method for highfrequency wave propagation. The derivation of the method is based on asymptotic analysis. In this paper, for general linear strictly ...