Browsing by Subject "math.NA"
Now showing items 120 of 34

A convergent method for linear halfspace kinetic equations
(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
(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 Hybrid Globallocal Numerical Method for Multiscale PDEs
(20170423)We present a new hybrid numerical method for multiscale partial differential equations, which simultaneously captures both the global macroscopic information and resolves the local microscopic events. The convergence of ... 
A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations
This paper concerns the a priori generalization analysis of the Deep Ritz Method (DRM) [W. E and B. Yu, 2017], a popular neuralnetworkbased method for solving high dimensional partial differential equations. We derive ... 
A quasinonlocal coupling method for nonlocal and local diffusion models
(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 Surface Hopping Gaussian Beam Method for HighDimensional Transport Systems
(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 ... 
Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping
(20171130)To accelerate the thermal equilibrium sampling of multilevel quantum systems, the infinite swapping limit of a recently proposed multilevel ring polymer representation is investigated. In the infinite swapping limiting, ... 
An asymptotic preserving method for transport equations with oscillatory scattering coefficients
(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
(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 ... 
Bold Diagrammatic Monte Carlo in the Lens of Stochastic Iterative Methods
(20171130)This work aims at understanding of bold diagrammatic Monte Carlo (BDMC) methods for stochastic summation of Feynman diagrams from the angle of stochastic iterative methods. The convergence enhancement trick of the BDMC is ... 
ButterflyNet: 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. ... 
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 $\Omega(\sqrt{d}\, N^{3/2})$, ... 
Complexity of zigzag sampling algorithm for strongly logconcave distributions
We study the computational complexity of zigzag sampling algorithm for strongly logconcave distributions. The zigzag process has the advantage of not requiring time discretization for implementation, and that each ... 
Cubic scaling algorithms for RPA correlation using interpolative separable density fitting
(20170423)We present a new cubic scaling algorithm for the calculation of the RPA correlation energy. Our scheme splits up the dependence between the occupied and virtual orbitals in $\chi^0$ by use of Cauchy's integral formula. This ... 
Detecting localized eigenstates of linear operators
(20171130)We describe a way of detecting the location of localized eigenvectors of a linear system $Ax = \lambda x$ for eigenvalues $\lambda$ with $\lambda$ comparatively large. We define the family of functions $f_{\alpha}: \left\{1.2. ... 
Efficient construction of tensor ring representations from sampling
(20171130)In this note we propose an efficient method to compress a high dimensional function into a tensor ring format, based on alternating leastsquares (ALS). Since the function has size exponential in $d$ where $d$ is the number ... 
Existence and computation of generalized Wannier functions for nonperiodic systems in two dimensions and higher
Exponentiallylocalized Wannier functions (ELWFs) are a basis of the Fermi projection of a material consisting of functions which decay exponentially fast away from their maxima. When the material is insulating ... 
Fast algorithm for periodic density fitting for Bloch waves
(20170423)We propose an efficient algorithm for density fitting of Bloch waves for Hamiltonian operators with periodic potential. The algorithm is based on column selection and random Fourier projection of the orbital functions. The ... 
Frozen Gaussian approximation for high frequency wave propagation in periodic media
(20170426)Propagation of highfrequency wave in periodic media is a challenging problem due to the existence of multiscale characterized by short wavelength, small lattice constant and large physical domain size. Conventional computational ... 
Frozen Gaussian approximation with surface hopping for mixed quantumclassical dynamics: A mathematical justification of fewest switches surface hopping algorithms
(20170423)We develop a surface hopping algorithm based on frozen Gaussian approximation for semiclassical matrix Schr\"odinger equations, in the spirit of Tully's fewest switches surface hopping method. The algorithm is asymptotically ...