Research reports
Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991
Adaptive Approximation of Shapes
by A. Buffa and R. Hiptmair and P. Panchal
(Report number 2020-60)
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.
Keywords: Model reduction, shape calculus, shape gradient, shape Hessian, low-rank approximation, power iteration
BibTeX
@Techreport{BHP20_933,
author = {A. Buffa and R. Hiptmair and P. Panchal},
title = {Adaptive Approximation of Shapes},
institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
number = {2020-60},
address = {Switzerland},
url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2020/2020-60.pdf },
year = {2020}
}
Disclaimer
© Copyright for documents on this server remains with the authors.
Copies of these documents made by electronic or mechanical means including
information storage and retrieval systems, may only be employed for
personal use. The administrators respectfully request that authors
inform them when any paper is published to avoid copyright infringement.
Note that unauthorised copying of copyright material is illegal and may
lead to prosecution. Neither the administrators nor the Seminar for
Applied Mathematics (SAM) accept any liability in this respect.
The most recent version of a SAM report may differ in formatting and style
from published journal version. Do reference the published version if
possible (see SAM
Publications).