SHAPE OPTIMIZATION OF THE STOKES EIGENVALUE PROBLEM

Jiajie Li; Shengfeng Zhu

doi:10.1137/21M1451543

SHAPE OPTIMIZATION OF THE STOKES EIGENVALUE PROBLEM

Jiajie Li
, Shengfeng Zhu^*

^*Corresponding author for this work

School of Mathematical Sciences

Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice
East China Normal University

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

14 Scopus citations

Abstract

We consider solving the Stokes eigenvalue optimization problem. Distributed and boundary types of Eulerian derivatives are derived from shape calculus. A priori error estimates for finite element discretizations of both shape gradients are shown. The approximate distributed shape gradient has better convergence and is used in numerical algorithms. We propose a singlegrid algorithm and a two-grid algorithm for Stokes eigenvalue optimization. Numerical results are presented to verify theory and show effectiveness and efficiency of the algorithms proposed.

Original language	English
Pages (from-to)	A798-A828
Journal	SIAM Journal on Scientific Computing
Volume	45
Issue number	2
DOIs	https://doi.org/10.1137/21M1451543
State	Published - 2023

Keywords

Shape optimization
Stokes eigenvalue
distributed shape gradient
error estimate
mixed finite element

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10.1137/21M1451543

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title = "SHAPE OPTIMIZATION OF THE STOKES EIGENVALUE PROBLEM",

abstract = "We consider solving the Stokes eigenvalue optimization problem. Distributed and boundary types of Eulerian derivatives are derived from shape calculus. A priori error estimates for finite element discretizations of both shape gradients are shown. The approximate distributed shape gradient has better convergence and is used in numerical algorithms. We propose a singlegrid algorithm and a two-grid algorithm for Stokes eigenvalue optimization. Numerical results are presented to verify theory and show effectiveness and efficiency of the algorithms proposed.",

keywords = "Shape optimization, Stokes eigenvalue, distributed shape gradient, error estimate, mixed finite element",

author = "Jiajie Li and Shengfeng Zhu",

note = "Publisher Copyright: {\textcopyright} by SIAM.",

year = "2023",

doi = "10.1137/21M1451543",

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AU - Li, Jiajie

AU - Zhu, Shengfeng

N1 - Publisher Copyright: © by SIAM.

PY - 2023

Y1 - 2023

N2 - We consider solving the Stokes eigenvalue optimization problem. Distributed and boundary types of Eulerian derivatives are derived from shape calculus. A priori error estimates for finite element discretizations of both shape gradients are shown. The approximate distributed shape gradient has better convergence and is used in numerical algorithms. We propose a singlegrid algorithm and a two-grid algorithm for Stokes eigenvalue optimization. Numerical results are presented to verify theory and show effectiveness and efficiency of the algorithms proposed.

AB - We consider solving the Stokes eigenvalue optimization problem. Distributed and boundary types of Eulerian derivatives are derived from shape calculus. A priori error estimates for finite element discretizations of both shape gradients are shown. The approximate distributed shape gradient has better convergence and is used in numerical algorithms. We propose a singlegrid algorithm and a two-grid algorithm for Stokes eigenvalue optimization. Numerical results are presented to verify theory and show effectiveness and efficiency of the algorithms proposed.

KW - Shape optimization

KW - Stokes eigenvalue

KW - distributed shape gradient

KW - error estimate

KW - mixed finite element

UR - https://www.scopus.com/pages/publications/85156136094

U2 - 10.1137/21M1451543

DO - 10.1137/21M1451543

M3 - 文章

AN - SCOPUS:85156136094

SN - 1064-8275

VL - 45

SP - A798-A828

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 2

ER -

SHAPE OPTIMIZATION OF THE STOKES EIGENVALUE PROBLEM

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Keywords

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