Preprints

• 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, arXiv:2505.04120, submitted.

• 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, submitted.

• Yixin Tan, Fang Feng, and Shengfeng Zhu, Shape and topology optimization with phase field methods for structural hemivariational inequalities, submitted.

• Jiajie Li, Shengfeng Zhu, Energy stable gradient flow schemes for shape and topology optimization in Navier-Stokes flows, arXiv:2405.05098, submitted.

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

Publications

• 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, arXiv:2503.02440,  to appear, Nuclear Science and Techniques, 2025.

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

• 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.

• 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.

• Fang Feng, Hui Yang, Shengfeng Zhu, Modelling and numerical shape and topology  optimization for a hemivariational inequality in Stokes flows with slip boundary conditions, to appear, Communications in Computational Physics, 2025.

• 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, 2025.

• 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.