Browsing by Author "Ying, L"
Now showing items 1-8 of 8
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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 ... -
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 ... -
Crystal image analysis using 2D synchrosqueezed transforms
(Multiscale Modeling and Simulation, 2015-01-01)© 2015 Society for Industrial and Applied Mathematics.We propose efficient algorithms based on a band-limited version of 2D synchrosqueezed transforms to extract mesoscopic and microscopic information from atomic crystal ... -
Efficient construction of tensor ring representations from sampling
(2017-11-30)In this note we propose an efficient method to compress a high dimensional function into a tensor ring format, based on alternating least-squares (ALS). Since the function has size exponential in $d$ where $d$ is the number ... -
Fast construction of hierarchical matrix representation from matrix-vector multiplication
(Journal of Computational Physics, 2011-05-10)We develop a hierarchical matrix construction algorithm using matrix-vector multiplications, based on the randomized singular value decomposition of low-rank matrices. The algorithm uses O(logn) applications of the matrix ... -
Solving parametric PDE problems with artificial neural networks
(2017-11-30)The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modeled into the equations as random coefficients. However, very often ... -
Sparsifying preconditioner for soliton calculations
(Journal of Computational Physics, 2016-06-15)© 2016 Elsevier Inc.We develop a robust and efficient method for soliton calculations for nonlinear Schrödinger equations. The method is based on the recently developed sparsifying preconditioner combined with Newton's iterative ...
