  We study the space of $C^{2}$-smooth isogeometric functions on bilinearly
parameterized multi-patch domains $\Omega \subset \mathbb{R}^{2}$, where the
graph of each isogeometric function is a multi-patch spline surface of bidegree
$(d,d)$, $d \in \{5,6 \}$. The space is fully characterized by the equivalence
of the $C^2$-smoothness of an isogeometric function and the $G^2$-smoothness of
its graph surface, cf. (Groisser and Peters,2015; Kapl et al.,2015). This is
the reason to call its functions $C^{2}$-smooth geometrically continuous
isogeometric functions. In particular, the dimension of this $C^{2}$-smooth
isogeometric space is investigated. The study is based on the decomposition of
the space into three subspaces and is an extension of the work (Kapl and
Vitrih, 2017) to the multi-patch case. In addition, we present an algorithm for
the construction of a basis, and use the resulting globally $C^{2}$-smooth
functions for numerical experiments, such as performing $L^{2}$ approximation
and solving triharmonic equation, on bilinear multi-patch domains. The
numerical results indicate optimal approximation order.
