A level set method for shape optimization in semilinear elliptic problems

DOI10.1016/j.jcp.2017.09.066zbMath1380.49063OpenAlexW2767678133MaRDI QIDQ1700879

Xianliang Hu, Shengfeng Zhu, Qing-Biao Wu

Publication date: 22 February 2018

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2017.09.066

zbMATH Keywords

finite element methodsemilinear elliptic equationslevel set methodshape optimizationcharacteristic Galerkin finite element method

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Optimization of shapes other than minimal surfaces (49Q10) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (10)

On Geometric Inverse Problems in Time-Fractional Subdiffusion ⋮ A level set method for Laplacian eigenvalue optimization subject to geometric constraints ⋮ Modelling, analysis, and numerical methods for a geometric inverse source problem in variable-order time-fractional subdiffusion ⋮ Convergence analysis of Galerkin finite element approximations to shape gradients in eigenvalue optimization ⋮ Numerical reconstruction of a discontinuous diffusive coefficient in variable-order time-fractional subdiffusion ⋮ Numerical Shape Reconstruction for a Semi-Linear Elliptic Interface Inverse Problem ⋮ Effective shape optimization of Laplace eigenvalue problems using domain expressions of Eulerian derivatives ⋮ Convergence analysis of mixed finite element approximations to shape gradients in the Stokes equation ⋮ On accuracy of approximate boundary and distributed \(H^1\) shape gradient flows for eigenvalue optimization ⋮ A phase field method based on multi-level correction for eigenvalue topology optimization

Uses Software

• DistMesh

Cites Work

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