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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
(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
(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)
(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
(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
(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
We 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
(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
(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
(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
(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
(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
(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
(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
Deep 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
(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
We 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
(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
(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
(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
(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 ...
