Approximating Volumetric Shape Gradients for Shape Optimization with Curved Boundaries Constrained by Parabolic PDEs

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2025-09-23 DOI:10.1137/24m1681938

Leonardo Mutti, Michael Ulbrich

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 63, Issue 5, Page 2026-2047, October 2025.
Abstract. We quantify the accuracy of the approximate shape gradient for a shape optimization problem constrained by parabolic PDEs. The focus is on the volume form of the shape gradient, which is discretized using the finite element method and the implicit Euler scheme. Our estimate goes beyond previous work done in the elliptic setting and considers the error introduced by polygonal approximation of curved domains. Numerical experiments support the theoretical findings, and the code is made publicly available.

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抛物线偏微分方程约束下曲面边界形状优化的近似体积形状梯度

SIAM数值分析杂志，第63卷，第5期，第2026-2047页，2025年10月。摘要。我们量化了抛物线偏微分方程约束下的形状优化问题的近似形状梯度的精度。重点研究了形状梯度的体积形式，采用有限元法和隐式欧拉格式对其进行离散。我们的估计超越了以往在椭圆环境下所做的工作，并考虑了曲面域多边形近似所带来的误差。数值实验支持理论发现，代码已公开。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.