Numerical solution of the Falkner-Skan equation based on quasilinearization. - Shengfeng Zhu; Qingbiao Wu; Xiaoliang Cheng (Appl. Math. Comput., 2009)

Variational piecewise constant level set methods for shape optimization of a two-density drum. - Shengfeng Zhu; Qingbiao Wu; Chunxiao Liu (J. Comput. Phys., 2010)

A variational binary level-set method for elliptic shape optimization problems. - Shengfeng Zhu; Xiaoxia Dai; Chunxiao Liu (Int. J. Comput. Math., 2011)

New Variational Formulations for Level Set Evolution Without Reinitialization with Applications to Image Segmentation. - Chunxiao Liu; Fang-Fang Dong; Shengfeng Zhu; Dexing Kong; Kefeng Liu (J. Math. Imaging Vis., 2011)

An adaptive algorithm for the Thomas-Fermi equation. - Shengfeng Zhu; Hancan Zhu; Qingbiao Wu; Yasir Khan (Numer. Algorithms, 2012)

A convex relaxation method for computing exact global solutions for multiplicative noise removal. - Chunxiao Liu; Shengfeng Zhu (J. Comput. Appl. Math., 2013)

Inhomogeneous Dirichlet Boundary-Value Problems of Space-Fractional Diffusion Equations and their Finite Element Approximations. - Hong Wang 018; Danping Yang; Shengfeng Zhu (SIAM J. Numer. Anal., 2014)

Laguerre pseudospectral approximation to the Thomas-Fermi equation. - Chunxiao Liu; Shengfeng Zhu (J. Comput. Appl. Math., 2015)

Accuracy of Finite Element Methods for Boundary-Value Problems of Steady-State Fractional Diffusion Equations. - Hong Wang 018; Danping Yang; Shengfeng Zhu (J. Sci. Comput., 2017)

Isogeometric analysis and proper orthogonal decomposition for parabolic problems. - Shengfeng Zhu; Luca Dedè; Alfio Quarteroni (Numerische Mathematik, 2017)

A multi-mesh finite element method for phase-field based photonic band structure optimization. - Shengyang Wu; Xianliang Hu; Shengfeng Zhu (J. Comput. Phys., 2018)

A level set method for shape optimization in semilinear elliptic problems. - Shengfeng Zhu; Xianliang Hu; Qingbiao Wu (J. Comput. Phys., 2018)

Effective Shape Optimization of Laplace Eigenvalue Problems Using Domain Expressions of Eulerian Derivatives. - Shengfeng Zhu (J. Optim. Theory Appl., 2018)

Shape identification in Stokes flow with distributed shape gradients. - Jiajie Li 003; Shengfeng Zhu (Appl. Math. Lett., 2019)

Proper orthogonal decomposition with SUPG-stabilized isogeometric analysis for reduced order modelling of unsteady convection-dominated convection-diffusion-reaction problems. - Richen Li; Qingbiao Wu; Shengfeng Zhu (J. Comput. Phys., 2019)

On accuracy of approximate boundary and distributed H1 shape gradient flows for eigenvalue optimization. - Shengfeng Zhu; Xianliang Hu; Qingbiao Wu (J. Comput. Appl. Math., 2020)

Isogeometric analysis for time-fractional partial differential equations. - Xindi Hu; Shengfeng Zhu (Numer. Algorithms, 2020)

RBF-FD solution for a financial partial-integro differential equation utilizing the generalized multiquadric function. - Fazlollah Soleymani; Shengfeng Zhu (Comput. Math. Appl., 2021)

A Two-Grid Binary Level Set Method for Eigenvalue Optimization. - Jing Zhang; Shengfeng Zhu; Chunxiao Liu; Xiaoqin Shen (J. Sci. Comput., 2021)

On Discrete Shape Gradients of Boundary Type for PDE-constrained Shape Optimization. - Wei Gong 005; Shengfeng Zhu (SIAM J. Numer. Anal., 2021)

A level set method for Laplacian eigenvalue optimization subject to geometric constraints. - Meizhi Qian; Shengfeng Zhu (Comput. Optim. Appl., 2022)

On Geometric Inverse Problems in Time-Fractional Subdiffusion. - Xindi Hu; Shengfeng Zhu (SIAM J. Sci. Comput., 2022)

Improved Discrete Boundary Type Shape Gradients for PDE-constrained Shape Optimization. - Wei Gong 005; Jiajie Li 003; Shengfeng Zhu (SIAM J. Sci. Comput., 2022)

Adaptive Computation of an Elliptic Eigenvalue Optimization Problem with a Phase-Field Approach. - Jing Li; Yifeng Xu; Shengfeng Zhu (CoRR, 2023)

Shape Optimization of the Stokes Eigenvalue Problem. - Jiajie Li 003; Shengfeng Zhu (SIAM J. Sci. Comput., 2023)

Error and stability estimates of a time-fractional option pricing model under fully spatial-temporal graded meshes. - Fazlollah Soleymani; Shengfeng Zhu (J. Comput. Appl. Math., 2023)

Numerical Reconstruction of a Discontinuous Diffusive Coefficient in Variable-Order Time-Fractional Subdiffusion. - Wei Fan; Xindi Hu; Shengfeng Zhu (J. Sci. Comput., 2023)

Numerical method for two-dimensional linearly elastic clamped plate model. - Xiaoqin Shen; Rongfang Wu; Shengfeng Zhu (Int. J. Comput. Math., 2023)

A numerical B-spline Galerkin method with proper generalized decomposition for reduced order modeling of partial differential equations. - Richen Li; Qingbiao Wu; Shengfeng Zhu (Commun. Nonlinear Sci. Numer. Simul., 2024)

Energy stable gradient flow schemes for shape and topology optimization in Navier-Stokes flows. - Jiajie Li 003; Shengfeng Zhu (CoRR, 2024)

An adaptive phase-field method for structural topology optimization. - Bangti Jin; Jing Li; Yifeng Xu; Shengfeng Zhu (J. Comput. Phys., 2024)

Shape optimization with virtual element method. - Fang Feng; Hui Yang; Shengfeng Zhu (Commun. Nonlinear Sci. Numer. Simul., 2024)

Topology optimization of Stokes eigenvalues by a level set method. - Jiajie Li; Meizhi Qian; Shengfeng Zhu (Comput. Math. Appl., 2025)

Topology optimization of the two smallest p-Laplacian eigenvalues by a level set method. - Jing Li; Meizhi Qian; Shengfeng Zhu (Commun. Nonlinear Sci. Numer. Simul., 2025)

Numerical Shape Optimization of an Isothermal Compressible Navier-Stokes Flow. - Keyang Zhang; Jiajie Li; Shengfeng Zhu (J. Optim. Theory Appl., 2025)

Adaptive Finite Element Approximations of the First Eigenpair Associated with ({p} )-Laplacian. - Guanglian Li; Jing Li; Julie Merten; Yifeng Xu; Shengfeng Zhu (SIAM J. Sci. Comput., 2025)

Artificial Intelligence in Reactor Physics: Current Status and Future Prospects. - Ruizhi Zhang; Shengfeng Zhu; Kan Wang; Ding She; Jean-Philippe Argaud; Bertrand Bouriquet; Qing Li; Helin Gong (CoRR, 2025)

On the Crouzeix-Raviart Finite Element Approximation of Phase-Field Dependent Topology Optimization in Stokes Flow. - Bangti Jin; Jing Li; Yifeng Xu; Shengfeng Zhu (CoRR, 2025)

Convergence Analysis of an Adaptive Nonconforming FEM for Phase-Field Dependent Topology Optimization in Stokes Flow. - Bangti Jin; Jing Li; Yifeng Xu; Shengfeng Zhu (CoRR, 2025)