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Engineering with Computers
Erschienen in: Engineering with Computers 4/2014

01.10.2014 | Original Article

Conformal parameterization for multiply connected domains: combining finite elements and complex analysis

verfasst von: Everett Kropf, Xiaotian Yin, Shing-Tung Yau, Xianfeng David Gu

Erschienen in: Engineering with Computers | Ausgabe 4/2014

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Abstract

Conformal parameterization plays an important role in isogeometric analysis. Genus zero surfaces with multiple boundary components (multiply connected domains) can be conformally mapped onto planar domains with circular holes (circle domains). This work introduces a novel method to compute such conformal mappings combining finite element and complex analysis methods. First, the surface is mapped to planar annulus with concentric circular slits using holomorphic differentials, which is carried out using a finite element method based on Hodge decomposition; second the slit domain is conformally mapped to a circle domain by a Laurent series method. Compared with existing algorithms, the proposed method is more efficient and robust. Numerical experiments demonstrate the efficiency and efficacy of the method.
Vorheriger Artikel Volumetric T-spline construction using Boolean operations
Nächster Artikel A new method for T-spline parameterization of complex 2D geometries

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Fußnoten
1
To see this, transform C j to the real axis by a Möbius map, where reflection is simply complex conjugation, and then invert the previously applied Möbius map.
 
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Metadaten
Titel
Conformal parameterization for multiply connected domains: combining finite elements and complex analysis
verfasst von
Everett Kropf
Xiaotian Yin
Shing-Tung Yau
Xianfeng David Gu
Publikationsdatum
01.10.2014
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 4/2014
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-013-0348-4

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