Adaptive Approximation of Shapes. (4th December 2021)

• Record Type: Journal Article
• Authors: Buffa, A.; Hiptmair, R.; Panchal, P.
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 2(2021)
• Page Start: 132
• Page End: 154
• Publication Date: 2021-12-04
• Subjects: Model reduction -- shape calculus -- shape gradient -- shape Hessian -- low-rank approximation -- power iteration; 49Q10 -- 65F55; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1870134
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: We consider scalar-valued shape functionals on sets of shapes which are small perturbations of a reference shape. The shapes are described by parameterizations and their closeness is induced by a Hilbert space structure on the parameter domain. We justify a heuristic for finding the best low-dimensional parameter subspace with respect to uniformly approximating a given shape functional. We also propose an adaptive algorithm for achieving a prescribed accuracy when representing the shape functional with a small number of shape parameters.