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  • Isogeometric analysis with geometrically continuous functions on two-patch geometries
    Kapl, 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 odrasle
    Leto - 2015
    Jezik - angleški
    COBISS.SI-ID - 1537819588

    Povezava(-e):

    http://dx.doi.org/10.1016/j.camwa.2015.04.004
    Repozitorij Univerze na Primorskem - RUP
    DOI

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