Projects per year
Personal profile
Personal profile
I study iterative methods for numerical solution of partial differential equations, in particular, domain decomposition methods for the linear wave equation.
Research interests
Numerical Solvers for Waves
Parallel Computing
Domain Decomposition and Multigrid Methods
Numerical Analysis and Scientific Computing
Experience
Associate Professor, Department of Mathematical Sciences - Xian Jiaotong-Liverpool University - 2019 to present
Lecturer, Department of Mathematics - Zhejiang Ocean University - 2015-2019
Postdoc, Section de Mathématiques - Université de Genève - 2010-2015
Lecturer, School of Mathematical Sciences - University of Electronic Sciences and Technology of China - 2008-2010
Teaching
SURF (Summer Undergraduate Research Fund) Numericcal Analysis (2023 Summer, advising 5 students; 2024 Summer, 3 students)
MTH321 Numerical Analysis of Partial Differential Equations (2023-2024 Semester 1, module leader, sole teacher, first realization of a new module; 24-25-S1, module leader, sole teacher, integrating AI)
MTH301 Final Year Project (2022-2023, 6 students on data analysis of Chinese stock market and numerical analysis of PDEs)
MTH208 Numerical Analysis (2022-2023 Semester 2)
MTH301 Final Year Project (2022-2023) 6 students on data analysis of Chinese stock market and numerical analysis of PDEs
MTH208 Numerical Analysis (2022-2023 Semester 2, first realization after module spec majorly modified, wrote a new set of labs and slides)
MTH017 Linear Algebra for Mathematical Sciences (2022-2023 Semester 1, HyFlex with iPad, wrote for my class a completely new set of notes/slides/tutorials/solutions)
MTH301 Finay Year Project (2021-2022) 5 students on data analysis of Chineses stock market and numerical analysis of matrix
MTH208 Numerical Analysis (2021-2022 Semester 2, online, a new set of lab videos/assignments/tutorial videos)
MTH107 Advanced Linear Algebra (2021-2022 Semester 1, whiteboard)
MTH301 Final Year Project (2020-2021) 3 students on data analysis of Chinese stock market and customer behavior
MTH208 Numerical Analysis (2020-2021 Semester 2, module leader, whiteboard+slides)
MTH017 Linear Algebra for Mathematical Sciences (2020-2021 Semester 1, module leader, blended teaching, completely new lec videos/assignments/quizzes/tutorials))
MTH301 Final Year Project (2019-2020) 1 student on data analysis of Chinese stock market
MTH118 Analysis 2 (2019-2020 Semester 2, online, a new set of assignments/quizzes)
MTH017 Linear Algebra for Mathematical Sciences (2019-2020 Semester 1, whiteboard)
Awards and honours
2018 Plenary Speaker, 25th International Conference on Domain Decomposition Methods, St. Johns, Newfoundland, Canada
Education/Academic qualification
PhD, Xi'an Jiaotong University - 2008
BSc, Xi'an Jiaotong University - 2002
Research areas
- Numerical Analysis
- Scientific Machine Learning
- Parallel Computing
- Domain Decomposition Methods
- Helmholtz Equation
- Preconditioner
- Maxwell's Equations
Person Types
- Staff
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Collaborations and top research areas from the last five years
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Projects
- 9 Finished
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What are the Computing Skills of Future Applied Mathematicians? Use of Generative AI in Computer Labs of a Mathematical Module based on Student Partnership
Zhang, H. (PI), Wang, Y. (CoI) & Niu, Q. (CoI)
1/09/24 → 31/08/25
Project: Internal Research Project
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Fast Iterative Solvers for the Wave Problems
Zhang, H. (PI)
1/09/20 → 31/08/24
Project: Internal Research Project
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Machine Learning-based Generalized Multiscale Finite Element Method with Application in Reservoir Simulation
Chen, J. (PI), Ma, F. (Team member), Niu, Q. (Team member), Zhang, H. (Team member), 朱圣鑫 (Team member), 陈掌星 (Team member), 吴邦玉 (Team member), 王瑞 (Team member), 李博 (Team member) & 郑浩 (Team member)
1/01/20 → 31/12/22
Project: Internal Research Project
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High performance preconditioning techniques for the numerical simulation of complex dynamic fluids
Niu, Q. (PI), Ma, F. (Team member), Liu, G. (Team member), Zhang, H. (Team member), Ma, E. (Team member), Liang, H. (Team member), 朱圣鑫 (Team member), 申槟瑞 (Team member) & 侯思泽 (Team member)
1/07/19 → 30/06/22
Project: Internal Research Project
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Direct Discontinuous Galerkin Methods for Interface Problems and Applications
Huang, H. (PI) & Zhang, H. (CoPI)
1/01/18 → 31/12/21
Project: Governmental Research Project
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Heterogeneous Optimized Schwarz Methods for Heat Conduction in Composites with Thermal Contact Resistance
Zhang, H., Zhang, H., Wang, Y. & Xu, Y., Aug 2026, In: East Asian Journal on Applied Mathematics. 16, 3, p. 632-661 30 p.Research output: Contribution to journal › Article › peer-review
Open Access -
Multiscale Subsurface Flow in the Era of Deep Learning: A Review
Li, P., Chen, J., Zhang, H. & Hands, S., 2 Apr 2026, (Submitted) In: SSRN Online Journal.Research output: Contribution to journal › Review article
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Convergence analysis of a solver for the linear Poisson--Boltzmann model
Liu, X., Maday, Y., Quan, C. & Zhang, H., 10 Jun 2025, In: SIAM Journal on Numerical Analysis. 63, 3, p. 1232-1253 22 p.Research output: Contribution to journal › Article › peer-review
Open Access -
Fourier beyond dispersion: Wavenumber explicit and precise accuracy of FDMs for the Helmholtz equation
Zhang, H., Sept 2025, In: Applied Mathematics Letters. 168, 109576.Research output: Contribution to journal › Article › peer-review
3 Citations (Scopus) -
Confluent Vandermonde with Arnoldi
Niu, Q., Zhang, H. & Zhou, Y., Jan 2023, In: Applied Mathematics Letters. 135, 108420.Research output: Contribution to journal › Article › peer-review
3 Citations (Scopus)
Activities
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A New Hierarchical Domain Decomposition Method with Coarse Correction: From Poisson to Helmholtz Problems
Zhang, H. (Speaker)
19 Jun 2026Activity: Talk or presentation › Presentation at conference/workshop/seminar
File -
Convergence Analysis of a Solver for the Linear Poisson–Boltzmann Model
Zhang, H. (Speaker)
13 Jun 2026Activity: Talk or presentation › Presentation at conference/workshop/seminar
File -
Hierarchical Basis by Randomised SVD
Zhang, H. (Speaker)
27 Dec 2025Activity: Talk or presentation › Invited talk
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Numerical investigation on some coarse problem for wave propagation
Zhang, H. (Speaker)
27 Jun 2025Activity: Talk or presentation › Presentation at conference/workshop/seminar
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Compact high order schemes by interpolation with polynomials and plane waves
Zhang, H. (Speaker)
24 Jun 2025Activity: Talk or presentation › Presentation at conference/workshop/seminar