Engineering analysis error estimation when removing finite-sized features in nonlinear elliptic problems

Li, Ming, Gao, Shuming and Martin, Ralph Robert 2013. Engineering analysis error estimation when removing finite-sized features in nonlinear elliptic problems. Computer-Aided Design 45 (2) , pp. 361-372. 10.1016/j.cad.2012.10.019

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Abstract

The paper provides novel approaches for a posteriori estimation of goal-oriented engineering analysis error caused by removing finite-sized negative features from a complex model, in the case of analysis of nonlinear elliptic physical phenomena. The features may lie within the model’s interior or along its boundary, and may be constrained with either Neumann or Dirichlet boundary conditions. The main use is for deciding whether detail design features can be removed from a model, to simplify meshing and engineering analysis, without unduly affecting analysis results. Error estimates are found using adjoint theory. Using a rigorous mathematical derivation, the error is first reformulated as a local quantity defined over the boundary of the feature to be suppressed, via linearization and Green’s theorem. This intermediate result still involves unknown terms, which we overcome in three ways. In one, an approximate upper bound of the error is obtained rigorously utilizing classical theories of differential operators; the others are heuristic practical approaches. The performance and the effectivity of these three different approaches are examined on 2D and 3D internal and boundary features, with Neumann and Dirichlet boundary conditions.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA76 Computer software
Uncontrolled Keywords:	Modification error; Defeaturing; Analysis-dependent simplification; Semilinear elliptic equation; CAD/CAE integration
Additional Information:	PDF uploaded in accordance with publisher's policy http://www.sherpa.ac.uk/romeo/issn/0010-4485/ [accessed 29/05/2015] NOTICE: this is the author’s version of a work that was accepted for publication in Computer-Aided Design. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer-Aided Design, [VOL 45, ISSUE 2, 2013] DOI 10.1016/j.cad.2012.10.019
Publisher:	Elsevier
ISSN:	0010-4485
Last Modified:	05 Dec 2024 09:30
URI:	https://orca.cardiff.ac.uk/id/eprint/42169

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