Preprints

• Jiajie Li, Xiang Ji, Shenggao Zhou, Shengfeng Zhu, Maximization of Supercapacitor Storage via Topology Optimization of Electrode Structures, arXiv:2511.20969, submitted.

• Jing Li, Xindi Hu, Helin Gong, Wei Gong, and Shengfeng Zhu, A Unified Phase-Field Fourier Neural Network Framework for Topology Optimization, arXiv:2511.14623, submitted.

• Zongyuan Liu, Jiajie Li, Shengfeng Zhu, Topology optimization for microfluidic mixers by a phase field method,

  preprint arXiv:2510.19192, submitted.

• Xindi Hu, Jiaming Weng, Shengfeng Zhu, Adversarial neural network methods for topology optimization of eigenvalue problems, arXiv:2405.06248 2024, submitted.

Publications

• Jiajie Li, Hui Yang, and Shengfeng Zhu, Topology Optimization in Thermal-Fluid Coupling by a Phase-Field Method, accepted by SIAM Journal on Control and Optimization, 2026.

• Bangti Jin, Jing Li, Yifeng Xu, and Shengfeng Zhu, Convergence analysis of an adaptive nonconforming FEM for phase-field dependent topology optimization in Stokes flow, Mathematics of Computation, DOI: https://doi.org/10.1090/mcom/4192, 2026.

• Ruizhi Zhang, Shengfeng Zhu, Kan Wang, Ding She, Jean-Philippe Argaud, Bertrand Bouriquet, Qing Li, Helin Gong, Artificial Intelligence in Reactor Physics: Current Status and Future Prospects, Nuclear Science and Techniques, Volume 37, article number 100, 2026.

• Qianqian Wu, Rongfang Gong, Wei Gong, Ziyi Zhang, and Shengfeng Zhu, Bioluminescence tomography via a shape optimization method based on a complex-valued model,  Inverse Problems, Volume 42, 035008, 2026

• Jiajie Li, Yixin Tan, and Shengfeng Zhu, Superconvergence analysis for patch-recovered finite element approximations of topological derivatives, IMA Journal of Numerical Analysis, draf121 (2026).

• Jiajie Li, Hui Yang, Jiayi Ye, and Shengfeng Zhu, Shape and topology optimization for solving a random Bernoulli free boundary problem based on the Multimodes Monte Carlo method, International Journal for Uncertainty Quantification, Volume 16, Issue 1, (2026) 1-28.

• Bangti Jin, Jing Li, Yifeng Xu, and Shengfeng Zhu, On the Crouzeix-Raviart Finite Element Approximation of Phase-Field Dependent Topology Optimization in Stokes Flow, International Journal for Numerical Methods in Engineering, Volume126, Issue21, (2025) e70197.

• Jiajie Li, Hui Yang, and Shengfeng Zhu, Efficient Multimodes Monte Carlo Method for Structural Topology Optimization With Random Uncertainties, International Journal for Numerical Methods in Engineering, Volume126, Issue21, (2025) e70172.

• Wei Fan and Shengfeng Zhu, Modeling, analysis, and numerical methods for shape identification of moving geometric inverse source and potential of parabolic problems, Inverse Problems, Volume 41, 105005, 2025

• Naping Bao, Shengfeng Zhu, and Helin Gong, Spatiotemporal GEIM for Ultra-real-time Prediction of Coupled Multi-Physics in Reactor Transients Using Sparse Observations, Journal of Computational Physics, Volume 543, 114401, 2025.

• Jiajie Li, Hui Yang, and Shengfeng Zhu, An unconditionally energy stable gradient flow for phase field modelling of structural topology optimization in geometrically nonlinear elasticity, Journal of Scientific Computing, 104 (2025) article number 108, 36 pp.

• Fang Feng, Hui Yang, Shengfeng Zhu, Modelling and numerical shape and topology  optimization for a hemivariational inequality in Stokes flows with slip boundary conditions, Communications in Computational Physics, 38 (2025) 850-886.

• Jiajie Li, Wan Li, Shengfeng Zhu, Convergence analysis of approximate shape gradients for shape optimization in parabolic problems, ESAIM: Mathematical Modelling and Numerical Analysis. 59 (2025) 2141–2170.

• Jiangnan Hou, Jiajie Li, Shengfeng Zhu, Xindi Hu, Zeyang Yu, Parallel computing on GPU with CuPy and vectorized SpMV for large-scale topology optimization, Finite Elements in Analysis and Design, 250 (2025) 104388. 

• Fazlollah Soleymani, Shengfeng Zhu, and Mahdiar Barfeie, On convergence of integrated radial basis function approximations on specific stencils with applications, Journal of Applied Mathematics and Computing, 2025.

• Xindi Hu, Yangwen Zhang, and Shengfeng Zhu, Efficient identification of geometric inverse sources of parabolic problems by model order reduction, Inverse Problems, 41 (2025) 055015.

• Jiajie Li, Shenggao Zhou, Shengfeng Zhu, Shape optimization of supercapacitor electrode to maximize charge storage, International Journal for Numerical Methods in Engineering, 126 (2025) e70052.

• Jing Li, Meizhi Qian, and Shengfeng Zhu, Topology optimization of the two smallest p-Laplacian eigenvalues by a level set method, Communications in Nonlinear Science and Numerical Simulation, 147 (2025) 108854.

• Jiajie Li, Meizhi Qian, and Shengfeng Zhu, Topology optimization of Stokes eigenvalues by a level set method, Computers and Mathematics with Applications, 188 (2025) 50-71.

• Jiajie Li, Shengfeng Zhu, Energy stable gradient flow schemes for shape and topology optimization in Navier-Stokes flows, Communications in Computational Physics. 38 (2025) 404-438.

• Keyang Zhang, Jiajie Li, and Shengfeng Zhu, Numerical shape optimization of an isothermal compressible Navier-Stokes flow, Journal of Optimization Theory and Applications, 205 (2025)  article number 35.

• Xindi Hu, Helin Gong, and Shengfeng Zhu, A multi-scale finite element method for neutron transport eigenvalue problem, Nuclear Engineering and Technology, 2025, 103420

• Jing Li, Yifeng Xu, Shengfeng Zhu, Adaptive computation of an elliptic eigenvalue optimization problem with a phase-field approach, Journal of Numerical Mathematics, 33 (2025), no. 4, 337-373.

• Guanglian Li, Jing Li, Julie Merten, Yifeng Xu, Shengfeng Zhu, Adaptive finite element approximations of the first eigenpair associated with p-Laplacian, SIAM Journal on Scientific Computing. 47 (2025) A374-A402.

• Yixin Tan, Lingkang Yan, and Shengfeng Zhu, Structural topology optimization in linear and nonlinear elasticity using a discontinuous Galerkin finite element method, Control and Cybernetics. 53 (2024) 283-315.

• Fazlollah Soleymani, Shengfeng Zhu, Convergence properties of the radial basis function-finite difference method on specific stencils with applications in solving partial differential equations, Engineering Analysis with Boundary Elements, 169, Part B, 2024, 106026.

• Fazlollah Soleymani, Shengfeng Zhu, and Xindi Hu, An unsupervised K-means machine learning algorithm via overlapping to improve the nodes selection, Engineering Analysis with Boundary Elements, 168  (2024) 105919.

• Keyang Zhang, Shengfeng Zhu, Jiajie Li, and Wenjing Yan, Shape gradient methods for shape optimization of an unsteady multiscale fluid-structure interaction model,  Journal of Geometric Analysis, 34 (2024) article number 245.

• Richen Li, Qingbiao Wu, and Shengfeng Zhu, A numerical B-spline Galerkin method with proper generalized decomposition for reduced order modeling of partial differential equations, Communications in Nonlinear Science and Numerical Simulation,137 (2024) 108057.

• Jing Zheng, Shengfeng Zhu, Fazlollah Soleymani, A new efficient parametric level set method based on radial basis function-finite difference for structural topology optimization, Computers & Structures, 291 (2024) 107364.

• Bangti Jin, Jing Li, Yifeng Xu, Shengfeng Zhu, An adaptive phase-field method for structural topology optimization, Journal of Computational Physics, 506 (2024), Paper No. 112932.

• Fang Feng, Hui Yang and Shengfeng Zhu, Shape optimization with virtual element method, Communications in Nonlinear Science and Numerical Simulation, 131 (2024), Paper No. 107876, 20 pp.

• Yixin Tan and Shengfeng Zhu, Numerical shape reconstruction for a semi-linear elliptic interface inverse problem, East Asian Journal on Applied Mathematics, 14 (2024) 147-178.

• Rongfang Wu, Xiaoqin Shen, Qian Yang and Shengfeng Zhu, A new a priori error estimation of the nonconforming elements for two-dimensional linear elastic shallow shell equations, Communications in Mathematical Sciences, 22 (2024) 167-179.

• Hui Yang and Shengfeng Zhu, Shape optimization of Stokes flows by a penalty method, Applied Numerical Mathematics, 196 (2024) 133-158.

• Xindi Hu, Meizhi Qian, and Shengfeng Zhu, Accelerating a phase field method by linearization for eigenfrequency topology optimization, Structural and Multidisciplinary Optimization, 66 (2023) article number 242.

• Xiaoqin Shen, Rongfang Wu, and Shengfeng Zhu, Numerical method for two-dimensional linearly elastic clamped plate model, International Journal of Computer Mathematics,100 (2023) 1779-1793.

• Yingyuan Li, Wenjing Yan, Shengfeng Zhu, and Feifei Jing, Optimal error estimates of the discrete shape gradients for shape optimizations governed by the Stokes-Brinkman equations, Applied Numerical Mathematics, 190 (2023) 220–253.

• Wei Fan, Xindi Hu, and Shengfeng Zhu, Modelling, analysis, and numerical methods for a geometric inverse source problem in variable-order time-fractional subdiffusion, Inverse Problems and Imaging 17 (2023) 767–797.

• Chunxiao Liu, Xianliang Hu, and Shengfeng Zhu, A two-grid binary level set method for structural topology optimization, Engineering Optimization, 55 (2023) 1100-1117.

• Yixin Tan and Shengfeng Zhu, A discontinuous Galerkin level set method using distributed shape gradient and topological derivatives for multi-material structural topology optimization, Structural and Multidisciplinary Optimization, 66 (2023) Article number: 170.

• Wei Fan, Xindi Hu, and Shengfeng Zhu, Numerical reconstruction of a discontinuous diffusive coefficient in variable-order time-fractional subdiffusion, Journal of Scientific Computing, 96 (2023), Paper No. 13, 33 pp.

• Chunxiao Liu and Shengfeng Zhu, On finite element approximations to a shape gradient flow in shape optimization of elliptic problems, Journal of Computational Mathematics, 41 (2023) 957–980.

• Jiajie Li and Shengfeng Zhu, Shape optimization of the Stokes eigenvalue problem, SIAM Journal on Scientific Computing 45 (2023) A798–A828.

• Jiajie Li, Shengfeng Zhu, and Xiaoqin Shen, On mixed finite element approximations of shape gradients in shape optimization with the Navier-Stokes equation, Numerical Methods for Partial Differential Equations 39 (2023) 1604-1634.

• Fazlollah Soleymani and Shengfeng Zhu, Error and stability estimates of a time-fractional option pricing model under fully spatial-temporal graded meshes, Journal of Computational and Applied Mathematics 45 (2023) Paper No. 115075, 17 pp.

• Xindi Hu and Shengfeng Zhu, On geometric inverse problems in time-fractional subdiffusion, SIAM Journal on Scientific Computing 44 (2022) A3560-A3591.

• Meizhi Qian, Xindi Hu, Shengfeng Zhu, A phase field method based on multi-level correction for eigenvalue topology optimization, Computer Methods in Applied Mechanics and Engineering 401 (2022) 115646.

• Jiajie Li, Shengfeng Zhu, Shape optimization of Navier–Stokes flows by a two-grid method, Computer Methods in Applied Mechanics and Engineering 400 (2022) 115531.

• Wei Gong, Jiajie Li, and Shengfeng Zhu, Improved discrete boundary type shape gradients for PDE-constrained shape optimization, SIAM Journal on Scientific Computing, 44 (2022) A2464-A2505.

• Meizhi Qian and Shengfeng Zhu, A level set method for Laplacian eigenvalue optimization subject to geometric constraints, Computational Optimization and Applications, 82 (2022) 499-524.

• Xiaoqin Shen, Yongjie Xue, Qian Yang, and Shengfeng Zhu, Finite element method coupling penalty method for flexural shell model, Advances in Applied Mathematics and Mechanics, 14 (2022) 365-385.

• Jiajie Li and Shengfeng Zhu, On distributed H1 shape gradient flows in optimal shape design of Stokes flows: convergence analysis and numerical applications, Journal of Computational Mathematics, 40 (2022) 232-258.

• Fazlollah Soleymani and Shengfeng  Zhu, On a high-order Gaussian radial basis function generated Hermite finite difference method and its application, Calcolo, 58 (2021) Paper No. 50, 22 pages.

• Jing Zhang, Shengfeng Zhu, Chunxiao Liu, and Xiaoqin Shen, A two-grid binary level set method for eigenvalue optimization, Journal of Scientific Computing, 89 (2021) Paper No. 57, 21 pages.

• Richen Li, Qingbiao Wu, and Shengfeng Zhu, Isogeometric analysis with proper orthogonal decomposition for elastodynamics, Communications in Computational Physics, 30 (2021) 396-422.

• Wei Gong and Shengfeng Zhu, On discrete shape gradients of boundary type for PDE-constrained shape optimization, SIAM Journal on Numerical Analysis, 59 (2021) 1510-1541.

• Fazlollah Soleymani and Shengfeng Zhu, RBF–FD solution for a financial partial–integro differential equation utilizing the generalized multiquadric function, Computers & Mathematics with Applications, 82 (2021) 161-178.

• Xindi Hu and Shengfeng Zhu, Isogeometric analysis for time-fractional partial differential equations, Numerical Algorithms, 85 (2020) 909-930.

• Shengfeng Zhu, Xianliang Hu, and Qifeng Liao, Convergence analysis of Galerkin finite element approximations to shape gradients in eigenvalue optimization. BIT Numerical Mathematics, 60 (2020) 853-878.

• Shengfeng Zhu, Xianliang Hu, Qingbiao Wu, On accuracy of approximate boundary and distributed H1 shape gradient flows for eigenvalue optimization. Journal of Computational and Applied Mathematics, 365 (2020), 112374.

• Jiajie Li, Shengfeng Zhu, Shape identification in Stokes flow with distributed shape gradients, Applied Mathematics Letters, 95 (2019) 165-171.

• Richen Li, Qingbiao Wu, Shengfeng Zhu: Proper orthogonal decomposition with SUPG-stabilized isogeometric analysis for reduced order modelling of unsteady convection-dominated convection-diffusion-reaction problems, Journal of Computational Physics, 387 (2019) 280-302.

• Pingfei Dai, Qingbiao Wu, Shengfeng Zhu: Quasi-Toeplitz splitting iteration methods for unsteady space-fractional diffusion equations, Numerical Methods for Partial Differential Equations, 35 (2019) 699-715.

• Xiaoqin Shen, Junjun Jia, Shengfeng Zhu, Haoming Li, Lin Bai, Tiantian Wang, Xiaoshan Cao: The time-dependent generalized membrane shell model and its numerical computation, Computer Methods in Applied Mechanics and Engineering, 344 (2019) 54-70.

• Shengfeng Zhu, Zhiming Gao: Convergence analysis of mixed finite element approximations to shape gradients in the Stokes equation,Computer Methods in Applied Mechanics and Engineering, 343 (2019) 127-150.

• Shengyang Wu, Xianliang Hu, Shengfeng Zhu: A multi-mesh finite element method for phase-field based photonic band structure optimization, Journal of Computational Physics, 357 (2018) 324-337.

• Shengfeng Zhu: Effective shape optimization of Laplace eigenvalue problems using domain expressions of Eulerian derivatives, Journal of Optimization Theory and Applications, 176 (2018) 17-34.

• Shengfeng Zhu, Xianliang Hu, Qingbiao Wu: A level set method for shape optimization in semilinear elliptic problems, Journal of Computational Physics, 355 (2018) 104-120.

• Shengfeng Zhu, Luca Dede, Alfio Quarteroni: Isogeometric analysis and proper orthogonal decomposition for the acoustic wave equation, ESAIM Mathematical Modelling and Numerical Analysis, 51 (2017) 1197-1221.

• Shengfeng Zhu, Luca Dede, Alfio Quarteroni: Isogeometric analysis and proper orthogonal decomposition for parabolic problems, Numerische Mathematik, 135 (2017) 333-370.

• Hong Wang, Danping Yang, Shengfeng Zhu: Accuracy of finite element methods for boundary-value problems of steady-state fractional diffusion equations, Journal of Scientific Computing, 70 (2017) 429-449.

• Hong Wang, Danping Yang, Shengfeng Zhu: A Petrov-Galerkin finite element method for variable-coefficient fractional diffusion equations, Computer Methods in Applied Mechanics and Engineering, 290 (2015) 45-56.

• Chunxiao Liu, Shengfeng Zhu: Laguerre pseudospectral approximation to the Thomas-Fermi equation, Journal of Computational and Applied Mathematics 282 (2015) 251-261. Matlab Code 

• Hong Wang, Danping Yang, Shengfeng Zhu: Inhomogeneous Dirichlet boundary-value problems of space-fractional diffusion equations and their finite element approximations, SIAM Journal on Numerical Analysis 52 (2014) 1292-1310. Matlab Package

• Chunxiao Liu, Shengfeng Zhu: A convex relaxation method to compute exact global solutions for multiplicative noise removal, Journal of Computational and Applied Mathematics 238 (2013) 144-155.

• Yi Peng, Shengfeng Zhu: Numerical asymptotic solutions to a class of singularly perturbed initial value problems, (Chinese) Commun. Appl. Math. Comput. 27 (2013) 363-371.

• Chunxiao Liu, Dexing Kong, Shengfeng Zhu: A primal-dual hybrid gradient algorithm to solve the LLT model for image denoising, Numerical Mathematics: Theory, Methods and Applications 5 (2012) 260-277.

• Shengfeng Zhu, Hancan Zhu, Qingbiao Wu, Yasir Khan: An adaptive algorithm for the Thomas-Fermi equation, Numerical Algorithms 59 (2012) 359-372.

• Chunxiao Liu, Fangfang Dong, Shengfeng Zhu, Dexing Kong, Kefeng Liu: New variational formulations for level set evolution without reinitialization with applications to image segmentation, Journal of Mathematical Imaging and Vision 41 (2011) 194-209.

• Shengfeng Zhu, Xiaoxia Dai, Chunxiao Liu: A variational binary level set method for elliptic shape optimization problems, International Journal of Computer Mathematics 88 (2011) 3026-3045.

• Shengfeng Zhu, Qingbiao Wu, Chunxiao Liu: Shape and topology optimization for elliptic boundary value problems using a variational piecewise constant level set method, Applied Numerical Mathematics 61 (2011) 752-767.

• Chunxiao Liu, Shengfeng Zhu: A semi-implicit binary level set method for source reconstruction problems, International Journal of Numerical Analysis and Modeling 8 (2011) 410-426.

• Shengfeng Zhu, Chunxiao Liu, Qingbiao Wu: Binary level set methods for topology and shape optimization of a two-density inhomogeneous drum, Computer Methods in Applied Mechanics and Engineering 199 (2010)  2970-2986.

• Shengfeng Zhu, Qingbiao Wu, Chunxiao Liu: Variational piecewise constant level set methods for shape optimization of a two-density drum, Journal of Computational Physics 229 (2010) 5062-5089.

• Shengfeng Zhu, Qingbiao Wu, Xiaoliang Cheng: Numerical solution of the Falkner-Skan equation based on quasilinearization, Applied Mathematics and Computation 215 (2009) 2472-2485.