Zhiguo Yang

About

My research lies in applied and computational mathematics, with a focus on scientific computing and numerical analysis. One central thread is the development of structure-preserving spectral and spectral-element algorithms for wave problems and electromagnetic systems, especially when divergence constraints, Gauss's law, or long-time stability are essential.

Since joining Shanghai Jiao Tong University in September 2020, I have developed a research program around three connected directions: structure-preserving high-order methods for electromagnetic wave problems; analytically solvable, asymptotic-preserving, and structure-preserving methods for electromagnetic-kinetic transport; and analysis and computation of complex condensed-matter systems, especially liquid crystals and moiré materials.

Spectral Methods Spectral-Element Methods Structure Preservation Multiscale PDEs Electromagnetic-Kinetic Transport Liquid Crystals Moiré Materials

Appointments and Education

2020–Present

Associate Professor
School of Mathematical Sciences, Shanghai Jiao Tong University

2017–2020

Golomb Visiting Assistant Professor
Purdue University

2017

Research Fellow
Nanyang Technological University

2012–2017

Ph.D. in Mathematics
Nanyang Technological University

Research Areas

Structure-Preserving Spectral and Spectral-Element Methods

Divergence-free spectral bases, Gauss's-law-preserving Maxwell solvers, curl-curl discretizations, and high-order methods for wave propagation and scattering in unbounded domains.

Electromagnetic-Kinetic Transport

Analytically solvable, asymptotic-preserving, and structure-preserving schemes for Vlasov-Poisson, Vlasov-Ampère, and Vlasov-Maxwell systems, including the ASAP framework for strongly oscillatory plasma regimes.

Liquid Crystals and Moiré Materials

Projection-type methods for quasiperiodic eigenvalue problems and rotational discrete-gradient schemes for constrained gradient flows and hydrodynamic liquid-crystal models.

Selected Publications

2026

An analytically-solvable, wave-form asymptotic-preserving and energy-conserving time-splitting scheme for Vlasov-Poisson equations in the quasi-neutral regime.

Yuanxiang Huang, Zhiguo Yang (corr). Journal of Computational Physics , 544, 114450.

2025

Low-dimensional compact states in 3D moiré lattices.

Zixuan Gao, Vladimir V. Konotop, Ruihan Peng, Zhenli Xu, Zhiguo Yang (co-corr), Fangwei Ye. Nature Communications , 16, 6306.

2024

A highly efficient and accurate divergence-free spectral method for the curl-curl equation in two and three dimensions.

Lechang Qin, Changtao Sheng, Zhiguo Yang (corr). SIAM Journal on Scientific Computing , 46(4), A2150–A2177.

2021

A truly exact and optimal perfect absorbing layer for time-harmonic acoustic wave scattering problems.

Zhiguo Yang , Li-Lian Wang, Yang Gao. SIAM Journal on Scientific Computing , 43(2), A1027–A1061.

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Teaching and Mentoring

My teaching emphasizes learning by doing, conceptual clarity, and intellectual independence. I have taught undergraduate and graduate courses in numerical methods, linear algebra, optimization methods, differential equations, and advanced computational methods.

I view research supervision as an extension of teaching: helping students formulate good questions, read efficiently, write clearly, and gradually grow into independent scholars.

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Selected Honors and Funding

Research Innovation Award, School of Mathematical Sciences, SJTU (2024).
Research Progress Award, School of Mathematical Sciences, SJTU (2023).
NSFC Science Fund for Excellent Young Scientists (Overseas) (2021).
Guo Benyu Young Scholar Outstanding Paper Award, First Prize (2020–2021 cycle).
National Key Research and Development Program for Young Scientists (2024–2029), Principal Investigator.