Browsing by Author "Lu, J"
Now showing items 1-20 of 71
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A convergent method for linear half-space kinetic equations
Li, Q; Lu, J; Sun, W (2017-04-23)We give a unified proof for the well-posedness of a class of linear half-space 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 (2017-11-30)Surface hopping algorithms are popular tools to study dynamics of the quantum-classical 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; Vanden-Eijnden, E (2017-04-23)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 Many-body Spin Dynamics
Cai, Z; Lu, J (2017-11-30)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 many-body ... -
A quasinonlocal coupling method for nonlocal and local diffusion models
Du, Q; Li, XH; Lu, J; Tian, X (2017-04-23)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 RBM-SVGD, 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 High-Dimensional Transport Systems
Cai, Z; Lu, J (2017-04-23)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, 2014-03-14)© Springer-Verlag 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 divergence-form elliptic ... -
Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation
Lin, L; Lu, J; Ying, L; E, W (Journal of Computational Physics, 2012-02-20)Kohn-Sham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the Kohn-Sham Hamiltonian generally results in a large number ... -
An asymptotic preserving method for transport equations with oscillatory scattering coefficients
Li, Q; Lu, J (2017-04-26)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 divide-and-conquer method for electronic structure calculations
Chen, J; Lu, J (2017-04-26)We study the accuracy of the divide-and-conquer 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 born-oppenheimer molecular dynamics
Lin, L; Lu, J; Shao, S (Entropy, 2014-01-01)We analyze the time reversible Born-Oppenheimer molecular dynamics (TRBOMD) scheme, which preserves the time reversibility of the Born-Oppenheimer molecular dynamics even with non-convergent self-consistent field iteration. ... -
Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model
Liu, JG; Lu, J; Margetis, D; Marzuola, JL (2017-04-23)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 ... -
Butterfly-Net: 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, 2016-04-01)© 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, 2015-12-01)© 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, 2016-12-29)This work considers the rigorous derivation of continuum models of step motion starting from a mesoscopic Burton–Cabrera–Frank-type model following the Xiang’s work (Xiang in SIAM J Appl Math 63(1):241–258, 2002). We prove ... -
Convergence of a Force-Based Hybrid Method in Three Dimensions
Lu, J; Ming, P (Communications on Pure and Applied Mathematics, 2013-01-01)We study a force-based hybrid method that couples an atomistic model with the Cauchy-Born elasticity model. We show that the proposed scheme converges to the solution of the atomistic model with second-order accuracy, since ... -
Convergence of frozen Gaussian approximation for high-frequency wave propagation
Lu, J; Yang, X (Communications on Pure and Applied Mathematics, 2012-06-01)The frozen Gaussian approximation provides a highly efficient computational method for high-frequency wave propagation. The derivation of the method is based on asymptotic analysis. In this paper, for general linear strictly ...