Shape optimization with virtual element method

Fang Feng; Hui Yang; Shengfeng Zhu

doi:10.1016/j.cnsns.2024.107876

Shape optimization with virtual element method

Fang Feng, Hui Yang^*, Shengfeng Zhu

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We present a new framework of partial differential equation (PDE)-constrained shape optimization with the virtual element method, which is less sensitive to the degenerated meshes with comparison to the conventional FEM utilized as PDE solvers for shape optimization in literature. Elliptic-type inverse problems, eigenvalue optimization, shape design of Stokes flows, and elastic structural optimization are considered as model problems. Numerical examples are presented to show the effectiveness of the shape-gradient type algorithm.

Original language	English
Article number	107876
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	131
DOIs	https://doi.org/10.1016/j.cnsns.2024.107876
State	Published - Apr 2024

Keywords

Elasticity
Polygonal meshes
Shape optimization
Stokes flows
Virtual element method

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10.1016/j.cnsns.2024.107876

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title = "Shape optimization with virtual element method",

abstract = "We present a new framework of partial differential equation (PDE)-constrained shape optimization with the virtual element method, which is less sensitive to the degenerated meshes with comparison to the conventional FEM utilized as PDE solvers for shape optimization in literature. Elliptic-type inverse problems, eigenvalue optimization, shape design of Stokes flows, and elastic structural optimization are considered as model problems. Numerical examples are presented to show the effectiveness of the shape-gradient type algorithm.",

keywords = "Elasticity, Polygonal meshes, Shape optimization, Stokes flows, Virtual element method",

author = "Fang Feng and Hui Yang and Shengfeng Zhu",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier B.V.",

year = "2024",

month = apr,

doi = "10.1016/j.cnsns.2024.107876",

language = "英语",

volume = "131",

journal = "Communications in Nonlinear Science and Numerical Simulation",

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T1 - Shape optimization with virtual element method

AU - Feng, Fang

AU - Yang, Hui

AU - Zhu, Shengfeng

PY - 2024/4

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N2 - We present a new framework of partial differential equation (PDE)-constrained shape optimization with the virtual element method, which is less sensitive to the degenerated meshes with comparison to the conventional FEM utilized as PDE solvers for shape optimization in literature. Elliptic-type inverse problems, eigenvalue optimization, shape design of Stokes flows, and elastic structural optimization are considered as model problems. Numerical examples are presented to show the effectiveness of the shape-gradient type algorithm.

AB - We present a new framework of partial differential equation (PDE)-constrained shape optimization with the virtual element method, which is less sensitive to the degenerated meshes with comparison to the conventional FEM utilized as PDE solvers for shape optimization in literature. Elliptic-type inverse problems, eigenvalue optimization, shape design of Stokes flows, and elastic structural optimization are considered as model problems. Numerical examples are presented to show the effectiveness of the shape-gradient type algorithm.

KW - Elasticity

KW - Polygonal meshes

KW - Shape optimization

KW - Stokes flows

KW - Virtual element method

UR - https://www.scopus.com/pages/publications/85183959834

U2 - 10.1016/j.cnsns.2024.107876

DO - 10.1016/j.cnsns.2024.107876

M3 - 文章

AN - SCOPUS:85183959834

SN - 1007-5704

VL - 131

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

M1 - 107876

ER -

Shape optimization with virtual element method

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Keywords

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