Preprints
-
Jiajie Li,
Shenggao Zhou, Shengfeng Zhu, Shape optimization of supercapacitor
electrode to maximize charge storage, arXiv:2406.09616, submitted.
-
Jiajie Li,
Shengfeng Zhu, Energy stable gradient flow schemes for shape and
topology optimization in Navier-Stokes flows, arXiv:2405.05098,
submitted.
-
Fazlollah
Soleymani, Shengfeng Zhu, On convergence of integrated radial basis
function approximations on specific stencils with applications,
submitted.
-
Xindi Hu,
Jiaming Weng, Shengfeng Zhu, Adversarial neural network methods for
topology optimization of eigenvalue problems, arXiv:2405.06248 2024,
submitted.
-
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
Publications
-
Jiajie Li,
Meizhi Qian, and Shengfeng Zhu, Topology optimization of Stokes
eigenvalues by a level set method, to appear,
Computers and Mathematics with Applications,
2025.
-
Keyang
Zhang, Jiajie Li, and Shengfeng Zhu, Numerical shape optimization of
an isothermal compressible Navier-Stokes flow,
to appear,
Journal of Optimization Theory and
Applications,
2025.
-
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.
-
-
-
-
-
-
-
-
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每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每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每980.
-
Jiajie Li
and Shengfeng Zhu,
Shape optimization of the Stokes eigenvalue
problem,
SIAM Journal on Scientific
Computing 45 (2023)
A798每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每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每FD solution for a financial partial每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.
-
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.
|