Adaptive Computation of Elliptic Eigenvalue Topology Optimization with a Phase-Field Approach

TL;DR

This paper presents an adaptive finite element method for elliptic eigenvalue topology optimization using a phase-field approach, demonstrating convergence and efficiency through numerical examples.

Contribution

It introduces an adaptive algorithm for elliptic eigenvalue optimization with a phase-field model, including theoretical convergence results and practical implementation.

Findings

The adaptive algorithm converges to the continuous optimal solution.

Numerical examples show the method's efficiency and accuracy.

Theoretical analysis confirms the vanishing limit of estimators.

Abstract

In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional numerical examples for illustration of efficiency and accuracy. Theoretical findings consist in the vanishing limit of a subsequence of estimators and the convergence of the relevant subsequence of adaptively-generated solutions to a solution to the continuous optimality system.