Mitigating spectral bias for the multiscale operator learning with hierarchical attention.
Xinliang Liu, Bo Xu, Lei Zhang,
J. Comput. Phys., accepted, 2024.
Preprint.
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Elastic far-field decay from dislocations in multilattices.
Dereck Olson, Chirstoph Ortner, Yangshuai Wang, Lei Zhang,
Multiscale Model. & Simul., 21(4), 1379-1409, 2023.
Preprint.
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A fast front-tracking approach and its analysis for a temporal multiscale flow problem with a fractional-order boundary growth based non-Newtonian hydrodynamic model.
Zhaoyang Wang, Ping Lin, Lei Zhang,
SIAM J. Sci. Comput., 45(5), B646-B672, 2023.
Preprint.
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Subspace decomposition based DNN algorithm for elliptic-type multi-scale PDEs.
Xi-An Li, Zhi-Qin John Xu, Lei Zhang,
J. Comput. Phys., 488, 112242, 2023.
Preprint.
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Adaptive multigrid strategy for large-scale molecular mechanics optimization.
Mingjie Liao, Yangshuai Wang, Kejie Fu, Jianjun Chen, Lei Zhang,
J. Comput. Phys., 485, 112113, 2023.
Preprint.
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On multilevel Monte Carlo methods for deterministic and uncertain hyperbolic systems.
Junpeng Hu, Shi Jin, Jinglai Li, Lei Zhang, submitted, 2022.
J. Comput. Phys., 475, 111847, 2023.
Preprint.
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Optimal control for multiscale PDEs with rough coefficients.
Yanping Chen, Xinliang Liu, Lei Zhang, Jiaoyan Zeng,
J. Comput. Math., 41, 842-866, 2023.
Preprint.
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DeePN2: A deep learning-based non-Newtonian hydrodynamic model.
Lidong Fang, Pei Ge, Lei Zhang, Huan Lei, Weinan E,
J. Mach. Learn., 1, 114-140, 2022.
Preprint.
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On the multiscale Landau-Lifshitz-Gilbert equation: Two-scale convergence and stability analysis.
Jingrun Chen, Rui Du, Zetao Ma, Zhiwei Sun, Lei Zhang,
Multiscale Model. Simul., 20(2), 835-856, 2022.
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Generalized rough polyharmonic splines for multiscale PDEs with rough coefficients.
Xinliang Liu, Lei Zhang, Shengxin Zhu,
Numer. Math. Theor. Meth. Appl., 14, 862-892, 2021.
Preprint.
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Iterated numerical homogenization for multi-scale elliptic equations with monotone nonlinearity.
Xinliang Liu, Eric Chung, Lei Zhang,
Multiscale Model. Simul., 19(4), 1601–1632, 2021.
Preprint.
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A posteriori error estimates for adaptive QM/MM coupling methods.
Yangshuai Wang, Huajie Chen, Mingjie Liao, Christoph Ortner, Hao Wang, Lei Zhang,
SIAM J. Sci. Comput., 43(4), A2785–A2808, 2021.
Preprint.
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Blended ghost force correction method for 3d crystalline defects.
Lidong Fang, Lei Zhang,
Commun. Comput. Phys., 29, 1246-1272, 2021.
Preprint.
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A priori analysis of a higher order nonlinear elasticity model for an atomistic chain with periodic boundary condition.
Yangshuai Wang, Hao Wang, Lei Zhang,
IMA J. Num. Anal., 41(2), 1465-1495, 2021.
Preprint.
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A DNN-based algorithm for multi-scale elliptic problems.
Xi'an Li, Zhiqin John Xu, Lei Zhang,
Commun. Comput. Phys., 1886-1906, special issue on "Machine learning for scientific computing", 2020.
Preprint.
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Surface anchoring controls orientation of a microswimmer in nematic liquid crystal.
Hai Chi, Mikhailo Potomkin, Lei Zhang, Igor Aronson, Leonid Berlyand,
Commun. Phys., 3, Article 162, 2020.
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Energy minimization and preconditioning in the simulation of athermal granular materials in two dimensions.
Haolei Wang, Lei Zhang,
Electron. Res. Arch., 28(1), 405-421, 2020.
Preprint.
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Surface, size and topological effects for some nematic equilibria on rectangular domains.
Lidong Fang, Apala Majumdar, Lei Zhang,
Math. Mech. Solid, 25(5), 1101-1123, 2020.
Preprint.
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A posteriori error estimate and adaptive mesh refinement algorithm for
atomistic/continuum coupling with finite range interactions in two dimensions.
Mingjie Liao, Ping Lin, Lei Zhang,
Commun. Comput. Phys., 27, 198-226, 2020.
Preprint.
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Fast eigenpairs computation with operator adapted wavelets and hierarchical subspace correction.
Hehu Xie, Lei Zhang, Houman Owhadi, SIAM J. Num. Anal. 57(6), 2519-2550, 2019.
Preprint.
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Adaptive QM/MM coupling for crystalline defects.
Huajie Chen, Mingjie Liao, Hao Wang, Yangshuai Wang, Lei Zhang, Comput. Methods Appl. Mech. Engrg., 354, 351-368, 2019.
Preprint.
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Optimizing parallel section length for small tensile specimen with fabrication non-uniformity in thickness.
Haiting Liu, Ran Chen, Mao Wen, Lei Zhang, Yao Shen, Fusion Eng. Des.,
147, 111244, 2019.
Preprint.
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A posteriori error estimation and adaptive algorithm for the atomistic/continuum coupling in 2D.
Hao Wang, Mingjie Liao, Ping Lin, Lei Zhang, SIAM J. Sci. Comput., 40(4), A2087–A2119, 2018.
Preprint.
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Experimental studies of vibrational modes in a two-dimensional amorphous solid.
Ling Zhang, Jie Zheng, Yinqiao Wang, Lei Zhang, Zhaohui Jin, Liang Hong, Yujie Wang, Jie Zhang,
Nature Commun., 8, Article 67, 2017.
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Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients.
Houman Owhadi, Lei Zhang,
J. Comput. Phys., 347, 99-128, 2017.
Preprint.
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A comprehensive solution to miniaturized tensile testing: Specimen geometry optimization and extraction of constitutive behaviors using inverse FEM procedure.
Haiting Liu, Yao Sheng, Shuang Yang, Pengfei Zheng, Lei Zhang, Fusion Eng. Des., 121, 188-197, 2017.
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Atomistic/continuum blending with ghost force correction.
Christoph Ortner, Lei Zhang, SIAM J. Sci. Comput., 38(1), A346-A375, 2016. Preprint.
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Effects of interface anisotropy and isotropic driving force on the
growth of steady-state shape in phase-field modeling.
Li Zhang, Yao Shen, Lei Zhang, et. al.,
Comput. Mat. Sci., 111, 313-321, 2016.
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On an evolution equation in a cell motility model.
Matthew S. Mizuhara, Leonid Berlyand, Volodymyr Rybalko, Lei Zhang,
Physica D: Nonlinear phenom., 318-319, 12-25, 2016.
Preprint.
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Domain decomposition preconditioner using rough polyharmonic splines.
Rui Du, Lei Zhang,
Chinese Ann. Math. Ser. B, 36(5), 803-812, as
Procccedings of the Shanghai Conference in honor of Professor Luc Tartar, 2015.
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Energy-based atomistic-to-continuum coupling without ghost forces.
C. Ortner, L. Zhang ,
Comput. Methods Appl. Mech. Engrg., 279 (1), 29-45, 2014.
Preprint.
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(In-)stability and stabilisation
of QNL-Type atomistic-to-continuum coupling methods.
C. Ortner, A. Shapeev, L. Zhang ,
Multiscale Model. Simul., 12 (3), 1258-1293, 2014.
Preprint.
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Polyharmonic homogenization, rough polyharmonic splines and sparse super-localization.
H. Owhadi, L. Zhang, L. Berlyand ,
ESAIM Math. Model. Numer. Anal. (M2AN), 48:2, 517-552, 2014.
Preprint.
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Construction and sharp consistency estimates for atomistic/continuum
coupling methods with general interfaces: a 2D model problem.
C. Ortner, L. Zhang ,
SIAM J. Numer. Anal., Volume 50, Issue 6, pp. 2940-2965, 2012.
Preprint.
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Localized bases for finite dimensional homogenization approximations
with non-separated scales and high-contrast.
H. Owhadi, L. Zhang ,
Multiscale Model. Simul., Volume 9, Issue 4, pp. 1373-1398, 2011.
Preprint.
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Global energy matching method for atomistic-to-continuum modeling of
self-assembling biopolymer aggregates.
L. Zhang, L. Berlyand, M. V. Fedorov, and H. Owhadi ,
Multiscale Model. Simul., Volume 8, Issue 5, pp. 1958-1980, 2010.
Preprint.
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Numerical homogenization of the accoustic wave equation with a continuum scales.
H. Owhadi, L. Zhang ,
Comput. Methods Appl. Mech. Engrg., Volume 198, Issues 3-4, Pages 397-406, Dec 15 2008.
Preprint.
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Homogenization of parabolic equations with a continuum space and time scales.
H. Owhadi, L. Zhang ,
SIAM J. Numer. Anal., Volume 46, Issue 1, pp. 1-36, 2007.
Preprint.
Movies (YouTube): u in euclidean coordinates,
u in caloric coordinates,
gradient of u in Euclidean coordinates,
gradient of u in caloric cooridinates,
image of fine mesh in caloric coordinates.
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Metric based upscaling.
H. Owhadi, L. Zhang ,
Commun. Pure Appl. Math., Vol. 60, Issue 5, p 675-723, 2007.
Preprint.
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Ghost Fluid方法与双介质可压缩流动计算.
张镭，袁礼,
计算物理, 20, 6, 503-508, 2003.
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用改进的耦合型Level Set方法计算一维双介质可压缩流动.
张镭, 袁礼,
计算物理, 18, 6, 511-516, 2001.
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