128 citations · 318 across the 17 of their papers we have counts for
18 papers
Convergence analysis of discrete high-index saddle dynamics
Yue Luo, Xiangcheng Zheng, Xiangle Cheng +1
Saddle dynamics is a time continuous dynamics to efficiently compute the any-index saddle points and construct the solution landscape. In practice, the saddle dynamics needs to be…
Uniform exponential contraction for viscous Hamilton-Jacobi equations
Konstantin Khanin, Ke Zhang, Lei Zhang
The well known phenomenon of exponential contraction for solutions to the viscous Hamilton-Jacobi equation in the space-periodic setting is based on the Markov mechanism. However,…
Generalized Rough Polyharmonic Splines for Multiscale PDEs with Rough Coefficients
Xinliang Liu, Lei Zhang, Shengxin Zhu
In this paper, we demonstrate the construction of generalized Rough Polyhamronic Splines (GRPS) within the Bayesian framework, in particular, for multiscale PDEs with rough coeffic…
Iterated numerical homogenization for multi-scale elliptic equations with monotone nonlinearity
Xinliang Liu, Eric Chung, Lei Zhang
Nonlinear multi-scale problems are ubiquitous in materials science and biology. Complicated interactions between nonlinearities and (nonseparable) multiple scales pose a major chal…
Optimal control for multiscale equations with rough coefficients
Yanping Chen, Jiaoyan Zeng, Xinliang Liu +1
This paper concerns the convex optimal control problem governed by multiscale elliptic equations with arbitrarily rough coefficients, which has important applications in…
Fast eigenpairs computation with operator adapted wavelets and hierarchical subspace correction
Hehu Xie, Lei Zhang, Houman Owhadi
We present a method for the fast computation of the eigenpairs of a bijective positive symmetric linear operator . The method is based on a combination of operator ada…
Multiscale Approach and The Convergence for the time-dependent Maxwell-Schrödinger System in Heterogeneous Nanostructures
Liqun Cao, Chupeng Ma, Jianlan Luo +1
This paper discusses the multiscale approach and the convergence of the time-dependent Maxwell-Schrödinger system with rapidly oscillating discontinuous coefficients arising from t…
A wavelet integral collocation method for nonlinear boundary value problems in Physics
Lei Zhang, Jizeng Wang, Xiaojing Liu +1
A high order wavelet integral collocation method (WICM) is developed for general nonlinear boundary value problems in physics. This method is established based on Coiflet approxima…
A high-precision method for general nonlinear initial-boundary value problems
Jizeng Wang, Lei Zhang, You-He Zhou
A high precision, and space time fully decoupled, wavelet formulation numerical method is developed for a class of nonlinear initial boundary value problems. This method is establi…
Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients
Houman Owhadi, Lei Zhang
Implicit schemes are popular methods for the integration of time dependent PDEs such as hyperbolic and parabolic PDEs. However the necessity to solve corresponding linear systems a…
Resonant equilibrium configurations in quasi-periodic media: KAM theory
Rafael de la Llave, Xifeng Su, Lei Zhang
We develop an a-posteriori KAM theory for the equilibrium equations for quasi-periodic solutions in a quasi-periodic Frenkel-Kontorova model when the frequency of the solutions res…
Resonant Equilibrium configurations in quasi-periodic media: perturbative expansions
Rafael de la Llave, Xifeng Su, Lei Zhang
We consider 1-D quasi-periodic Frenkel-Kontorova models. We study the existence of equilibria whose frequency (i.e. the inverse of the density of deposited material) is resonant wi…
Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization
Houman Owhadi, Lei Zhang, Leonid Berlyand
We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough () coefficient…
Localized bases for finite dimensional homogenization approximations with non-separated scales and high-contrast
Houman Owhadi, Lei Zhang
We construct finite-dimensional approximations of solution spaces of divergence form operators with -coefficients. Our method does not rely on concepts of ergodicity or s…
A novel boundary element method using surface conductive absorbers for full-wave analysis of 3-D nanophotonics
Lei Zhang, Jung Hoon Lee, Ardavan Oskooi +3
Fast surface integral equation (SIE) solvers seem to be ideal approaches for simulating 3-D nanophotonic devices, as these devices generate fields both in an interior channel and i…
Numerical Homogenization of the Acoustic Wave Equations with a Continuum of Scales
Houman Owhadi, Lei Zhang
In this paper, we consider numerical homogenization of acoustic wave equations with heterogeneous coefficients, namely, when the bulk modulus and the density of the medium are only…
Homogenization of parabolic equations with a continuum of space and time scales
Houman Owhadi, Lei Zhang
This paper addresses the issue of homogenization of linear divergence form parabolic operators in situations where no ergodicity and no scale separation in time or space are availa…
Metric based up-scaling
Houman Owhadi, Lei Zhang
We consider divergence form elliptic operators in dimension with coefficients. Although solutions of these operators are only Hölder continuous, we show that t…