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Isogeometric analysis with geometrically continuous functions on two-patch geometriesKapl, Mario ...We study the linear space of ▫$C^s$▫-smooth isogeometric functions defined on a multi-patch domain ▫$\Omega \subset \mathbb{R}^2$▫. 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 ▫$C^s$▫-smoothness of isogeometric functions is found to be equivalent to geometric smoothness of the same order (▫$G^s$▫-smoothness) of their graph surfaces. This motivates us to call them ▫$C^s$▫-smooth geometrically continuous isogeometric functions. We present a general framework to construct a basis and explore potential applications in isogeometric analysis. The space of ▫$C^1$▫-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 ▫$L^2$▫ approximation and for solving Poisson's equation and the biharmonic equation on two-patch geometries are presented and indicate optimal rates of convergence.Vir: Computers & mathematics with applications. - ISSN 0898-1221 (Vol. 70, iss. 7, 2015, str. 1518-1538)Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasleLeto - 2015Jezik - angleškiCOBISS.SI-ID - 1537819588
Avtor
Kapl, Mario |
Vitrih, Vito, 1981- |
Jüttler, Bert |
Birner, Katharina
Teme
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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vir: Computers & mathematics with applications. - ISSN 0898-1221 (Vol. 70, iss. 7, 2015, str. 1518-1538)
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Kapl, Mario | ![]() |
Vitrih, Vito, 1981- | 27559 |
Jüttler, Bert | ![]() |
Birner, Katharina | ![]() |
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