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

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.

32 pages, 14 figures, 2 tables, accepted by Journal of Numerical Mathematics

References in corpus (6)

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• An Adaptive Phase-Field Method for Structural Topology Optimization
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Cited by in corpus (3)

• Adaptive Approximations of Inclusions in a Semilinear Elliptic Problem Related to Cardiac Electrophysiology
• Convergence Analysis of an Adaptive Nonconforming FEM for Phase-Field Dependent Topology Optimization in Stokes Flow
• On the Crouzeix-Raviart Finite Element Approximation of Phase-Field Dependent Topology Optimization in Stokes Flow