  The first step towards applying isogeometric analysis techniques to solve PDE
problems on a given domain consists in generating an analysis-suitable mapping
operator between parametric and physical domains with one or several patches
from no more than a description of the boundary contours of the physical
domain. A subclass of the multitude of the available parameterization
algorithms are those based on the principles of Elliptic Grid Generation (EGG)
which, in their most basic form, attempt to approximate a mapping operator
whose inverse is composed of harmonic functions. The main challenge lies in
finding a formulation of the problem that is suitable for a computational
approach and a common strategy is to approximate the mapping operator by means
of solving a PDE-problem. PDE-based EGG is well-established in classical
meshing and first generalization attempts to spline-based descriptions (as is
mandatory in IgA) have been made. Unfortunately, all of the practically viable
PDE-based approaches impose certain requirements on the employed spline-basis,
in particular global $C^{\geq 1}$-continuity. This paper discusses a PDE-based
EGG-algorithm for the generation of planar parameterizations with arbitrary
continuity properties (where arbitrary stands for spline bases with global
$C^{\geq 0}$-continuity). A major use case of the proposed algorithm is that of
multi-patch parameterization, made possible by the support of $C^{\geq
0}$-continuities. This paper proposes a specially-taylored solution algorithm
that exploits many characteristics of the PDE-problem and is suitable for
large-scale applications. It is discussed for the single-patch case before
generalizing its concepts to multipatch settings. This paper is concluded with
three numerical experiments and a discussion of the results.
