| Title: | Isogeometric analysis with geometrically continuous functions on two-patch geometries |
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| Authors: | ID Kapl, Mario (Author)
ID Vitrih, Vito (Author)
ID Jüttler, Bert (Author)
ID Birner, Katharina (Author) |
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| Files: |  http://ac.els-cdn.com/S089812211500173X/1-s2.0-S089812211500173X-main.pdf?_tid=94ebf26e-65c7-11e5-a690-00000aacb361&acdnat=1443434537_5c4ed1d7a1642c0eac8eaa8cb06546b8
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | IAM - Andrej Marušič Institute
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| Abstract: | We study the linear space of Cs-smooth isogeometric functions defined on a multi-patch domain % % R2. We show that the construction of these functions is closely related to the concept of geometric continuity of surfaces, which has originated in geometric design. More precisely, the Cs-smoothness of isogeometric functions is found to be equivalent to geometric smoothness of the same order (Gs-smoothness) of their graph surfaces. This motivates us to call them Cs-smooth geometrically continuous isogeometric functions. We present a general framework to construct a basis and explore potential applications in isogeometric analysis. The space of C1-smooth geometrically continuous isogeometric functions on bilinearly parameterized two-patch domains is analyzed in more detail. Numerical experiments with bicubic and biquartic functions for performing L2 approximation and for solving Poisson%s equation and the biharmonic equation on two-patch geometries are presented and indicate optimal rates of convergence. |
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| Keywords: | izogeometrična analiza, geometrijska zveznost, geometrijsko vzezne izogeometrične funkcije, biharmonična enačba, isogeometric analysis, geometric continuity, geometrically continuous isogeometric functions, biharmonic equation, multi-patch domain |
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| Year of publishing: | 2015 |
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| Number of pages: | str. 1518-1538 |
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| Numbering: | Vol. 70, iss. 7 |
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| PID: | 20.500.12556/RUP-7159  |
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| ISSN: | 0898-1221 |
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| UDC: | 519.6 |
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| DOI: | 10.1016/j.camwa.2015.04.004 |
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| COBISS.SI-ID: | 1537819588 |
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| Publication date in RUP: | 15.10.2015 |
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| Views: | 3166 |
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| Downloads: | 192 |
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