个人简介
Students & Postdocs
Cuiwei Xue, PhD (Materials science), 2021-now, co-supervised with Prof. Yao Shen.
Xinyi Wei, PhD, 2021-now.
Zetao Mao, PhD, 2021-now.
Bo Xu, PhD, 2020-now.
Qinchen Song, PhD, 2020-now.
Junpeng Hu, PhD, 2020-now, co-supervised with Prof. Shi Jin.
Mingjie Liao, Postdoc, 2019-2021, currently researcher at AsiaInfo Technologies Limited, Beijing.
Xi'an Li, PhD, 2018-now.
Xingliang Liu, PhD, 2017-2021, postdoc at KAUST, Saudi Arabia, with Prof. Jinchao Xu.
Yangshuai Wang, PhD, 2016-2021, postdoc at UBC, Canada, with Prof. Christoph Ortner.
Peng Zhang, Postdoc (PhD Paris 12), 2015-2017, currently researcher at the Systems Engineering Research Institute, Beijing..
Lidong Fang, PhD, 2014-2020, postdoc at MSU, USA, with Prof. Huan Lei.
Haolei Wang, PhD, 2013-2020, engineer at China Electronics Technology Group Corporation.
Organizations
International Workshop on Mathematical Theory, Methods and Application in Materials Simulation at Shanghai Jiao Tong University, Apr 9-11, 2021
Multiscale Problems in Materials Science and Biology: Analysis and Computation at Tsinghua Sanya International Mathematics Forum (TSIMF), Jan 8-12, 2018
Short Course on Tensor Numerical Methods for Multidimensional PDEs, Apr. 06 - Apr. 12, 2017. Lectures 7-9, Lectures 10-11, Lectures 12, Lectures 13-14, Lectures 15, Matlab Exercises.
Workshop on Multiscale Modeling and Analysis in Materials Science -- A Satellite Meeting of ICIAM 2015, Aug 6-8, 2015
Workshop on Multiscale Problems from Physics, Biology and Materials Science, May 28-31, 2014
Workshop on Multiscale Modeling and Simulation in Materials Science, Apr 21-23, 2013
Grants
NSFC-DFG joint grant 12271360, PI, 2023-2026.
Shanghai Science and Technology Committee, PI, 2022-2025.
Shanghai Science and Technology Committee, co-PI, 2021-2023.
NSFC-DFG joint grant 11861131004, co-PI, 2019-2021.
NSFC grant 11871339, PI, 2019-2022.
NSFC grant 11571314, co-PI, 2016-2019.
Intel Higher Education research fund, PI, 2015-2016.
NSFC grant 11471214 (Construction, Analysis and Applications of Two Classes of Typical Multiscale Methods), PI, 2015-2018.
Thousand Talents Recruitment Program for Young Scientists, PI, 2013-2017.
Research Facilitation.
teaching
Using Julia
Using FreeFEM++
Using GSL Library
Teaching materials are mostly moved to Canvas after 2019.
Fall 2019: Scientific Computing
Canvas website
Class Information:
Office Hour: by appointment
Office Location: 329 Science Building
email: lzhang2012 AT sjtu
TA Office Hour:
TA Office Location: Graduate office, 5th floor Pao Yue-Kong Library
email: hlwang216 AT sjtu.edu.cn
Homework online: Thursday in even weeks
Homework due: Next Thursday in even weeks in class
Homework：20%
Quiz: 20%, Quiz 1 (Oct 29), Quiz 2 (Dec 10)
Final: 60%, Jan 2
Homework: (available before the separator ||)
Homework 1 (due Oct 12), Homework 2, Homework 3, Homework 4, Homework 5, Homework 6, Homework 7 ||
Exams:
Example Code in Julia:
Examples for Chapter 2 [View] [Download]
Examples for Chapter 3 [View] [Download]
Examples for Chapter 4 [View] [Download]
Examples for Chapter 5 [View] [Download]
Examples for Chapter 6 [View] [Download]
Examples for Chapter 7 [View] [Download]
References:
Textbook:
Numerical Mathematics by A. Quarteroni, R. Sacco, and F. Saleri
Other References:
数值分析, 张平文，李铁军编著，北京大学出版社
数值分析基础, 关治，陆金甫编著，高等教育出版社。
数值分析(第七版 影印版)，Burden, Faires, 高等教育出版社。
Iterative methods for sparse linear systems, Saad, SIAM, 2003.
Numerical Optimization, Nocedal, Wright, Springer, 2006
A First Course in the Numerical Analysis of Differential Equations, Iserles, Cambridge, 2008
Using Julia:
Julia official website: docs, examples, downloads, ...
Install Julia: Look at the part "Installing Julia and IJulia"
Juno: the interactive development environment for Julia
Numeric matrix manipulation: The cheat sheet for MATLAB, Python NumPy, R, and Julia
Noteworthy differences from MATLAB
Using FreeFEM++
FreeFEM++: A blazingly fast PDE solver
Using GSL Library
GNU Scientific Library:
GSL is written for Linux, 5 Ways to Run Linux Software on Windows, ortherwise, maybe you can figure out how to use GSL for Windows
How to compile & execute C programs under Linux (Absolute basics)
How to Debug C Program using gdb in 6 Simple Steps
Debugging Memory Problems with Valgrind (Advanced)
Unix tutorial for beginners
Undergraduate Teaching
Graduate School
Academic Information Service
Fall 2012: Numerical Methods for Differential Equations (Zhiyuan College)
Spring 2013: Numerical Methods for Partial Differential Equations (Mathematics Graduate)
Fall 2013: Probability (Zhiyuan ACM Class)
Spring 2014: Numerical Methods for Differential Equations (Zhiyuan College)
Spring 2014: Numerical Methods for Partial Differential Equations (Mathematics Graduate)
Spring 2015: Numerical Methods for Differential Equations (Zhiyuan College)
Spring 2016: Numerical Methods for Differential Equations (Zhiyuan College)
Spring 2016: Probability (Zhiyuan College)
Spring 2017: Numerical Methods for Differential Equations (Zhiyuan College)
Spring 2017: Numerical Methods for PDEs (Math Graduate)
Fall 2017: Scientific Computation (Math Graduate)
Spring 2018: Numerical Methods for Differential Equations (Zhiyuan College)
Spring 2019: Numerical Methods for Differential Equations (Zhiyuan College)
Spring 2019: Numerical Methods for PDEs (Math Graduate)
Using Julia
Using GSL Library
近期论文
查看导师新发文章
（温馨提示：请注意重名现象，建议点开原文通过作者单位确认）
Quantum algorithms for multiscale partial differential equations. Junpeng Hu, Shi Jin, Lei Zhang, submitted, 2023. Preprint.
Higher order far-field boundary conditions for crystalline defects. Julian Braun, Christoph Ortner, Yangshuai Wang, Lei Zhang, 2022. Preprint.
A posteriori error estimate and adaptivity for QM/MM models of crystalline defects. Yangshuai Wang, James R. Kermode, Christoph Ortner, Lei Zhang, 2022. Preprint.
HT-Net: Hierarchical Transformer based Operator Learning Model for Multiscale PDEs. Xinliang Liu, Bo Xu, Lei Zhang, submitted, 2022. Preprint.
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, submitted, 2022. Preprint.
Elastic far-field decay from dislocations in multilattices. Dereck Olson, Chirstoph Ortner, Yangshuai Wang, Lei Zhang, submitted, 2022. Preprint.
Subspace Decomposition based DNN algorithm for elliptic-type multi-scale PDEs. Xi-An Li, Zhi-Qin John Xu, Lei Zhang, submitted, 2021. Preprint.
Publications
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.
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.
Optimal control for multiscale PDEs with rough coefficients. Yanping Chen, Xinliang Liu, Lei Zhang, Jiaoyan Zeng, accepted by J. Comput. Math., 2022. Preprint.
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.
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.
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.
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.
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.
Blended ghost force correction method for 3d crystalline defects. Lidong Fang, Lei Zhang, Commun. Comput. Phys., 29, 1246-1272, 2021. Preprint.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Atomistic/continuum blending with ghost force correction. Christoph Ortner, Lei Zhang, SIAM J. Sci. Comput., 38(1), A346-A375, 2016. Preprint.
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.
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.
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.
Energy-based atomistic-to-continuum coupling without ghost forces. C. Ortner, L. Zhang , Comput. Methods Appl. Mech. Engrg., 279 (1), 29-45, 2014. Preprint.
(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.
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.
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.
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.
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.
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.
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.
Metric based upscaling. H. Owhadi, L. Zhang , Commun. Pure Appl. Math., Vol. 60, Issue 5, p 675-723, 2007. Preprint.
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.
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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