Isogeometric analysis with geometrically continuous functions on planar multi-patch geometries

Mario Kapl; Florian Buchegger; Michel Bercovier; Bert Jüttler

doi:10.1016/j.cma.2016.06.002

Isogeometric analysis with geometrically continuous functions on planar multi-patch geometries

Mario Kapl^*, Florian Buchegger, Michel Bercovier, Bert Jüttler

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

59 Scopus citations

Abstract

We generate a basis of the space of bicubic and biquartic C¹-smooth geometrically continuous isogeometric functions on bilinear multi-patch domains Ω⊂R². The basis functions are obtained by suitably combining C¹-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains (cf. [18]). They are described by simple explicit formulas for their spline coefficients. These C¹-smooth isogeometric functions possess potential for applications in isogeometric analysis, which is demonstrated by several examples (such as the biharmonic equation). In particular, the numerical results indicate optimal approximation power.

Original language	English
Pages (from-to)	209-234
Number of pages	26
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	316
DOIs	https://doi.org/10.1016/j.cma.2016.06.002
State	Published - 1 Apr 2017

Bibliographical note

Publisher Copyright:
© 2016 Elsevier B.V.

Keywords

Biharmonic equation
C-smooth isogeometric functions
Geometrically continuous isogeometric functions
Isogeometric analysis
Multi-patch domain

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10.1016/j.cma.2016.06.002

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title = "Isogeometric analysis with geometrically continuous functions on planar multi-patch geometries",

abstract = "We generate a basis of the space of bicubic and biquartic C1-smooth geometrically continuous isogeometric functions on bilinear multi-patch domains Ω⊂R2. The basis functions are obtained by suitably combining C1-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains (cf. [18]). They are described by simple explicit formulas for their spline coefficients. These C1-smooth isogeometric functions possess potential for applications in isogeometric analysis, which is demonstrated by several examples (such as the biharmonic equation). In particular, the numerical results indicate optimal approximation power.",

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AU - Kapl, Mario

AU - Buchegger, Florian

AU - Bercovier, Michel

AU - Jüttler, Bert

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N2 - We generate a basis of the space of bicubic and biquartic C1-smooth geometrically continuous isogeometric functions on bilinear multi-patch domains Ω⊂R2. The basis functions are obtained by suitably combining C1-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains (cf. [18]). They are described by simple explicit formulas for their spline coefficients. These C1-smooth isogeometric functions possess potential for applications in isogeometric analysis, which is demonstrated by several examples (such as the biharmonic equation). In particular, the numerical results indicate optimal approximation power.

AB - We generate a basis of the space of bicubic and biquartic C1-smooth geometrically continuous isogeometric functions on bilinear multi-patch domains Ω⊂R2. The basis functions are obtained by suitably combining C1-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains (cf. [18]). They are described by simple explicit formulas for their spline coefficients. These C1-smooth isogeometric functions possess potential for applications in isogeometric analysis, which is demonstrated by several examples (such as the biharmonic equation). In particular, the numerical results indicate optimal approximation power.

KW - Biharmonic equation

KW - C-smooth isogeometric functions

KW - Geometrically continuous isogeometric functions

KW - Isogeometric analysis

KW - Multi-patch domain

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SN - 0045-7825

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JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

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Isogeometric analysis with geometrically continuous functions on planar multi-patch geometries

Abstract

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