Adaptive finite element method for shape optimization

Pedro Morin, Ricardo H. Nochetto, Miguel S. Pauletti, Marco Verani

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Original languageEnglish (US)
Pages (from-to)1122-1149
Number of pages28
JournalESAIM: Control, Optimisation and Calculus of Variations
Volume18
Issue number4
DOIs
StatePublished - Jan 16 2012
Externally publishedYes

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