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This paper presents a PDE-based parameterisation framework for addressing theplanar surface-to-volume (StV) problem of finding a valid description of thedomain's interior given no more than a spline-based description of its boundarycontours. The framework is geared towards isogeometric analysis (IGA)applications wherein the physical domain is comprised of more than four sides,hence requiring more than one patch. We adopt the concept of harmonic maps andpropose several PDE-based problem formulations capable of finding a valid mapbetween a convex parametric multipatch domain and the piecewise-smooth physicaldomain with an equal number of sides. In line with the isoparametric paradigmof IGA, we treat the StV problem using techniques that are characteristic forthe analysis step. As such, this study proposes several IGA-based numericalalgorithms for the problem's governing equations that can be effortlesslyintegrated into a well-developed IGA software suite. We augment the frameworkwith mechanisms that enable controlling the parametric properties of theoutcome. Parametric control is accomplished by, among other techniques, theintroduction of a curvilinear coordinate system in the convex parametric domainthat, depending on the application, builds desired features into the computedharmonic map, such as homogeneous cell sizes or boundary layers.

PDE-Based Parameterisation Techniques for Planar Multipatch Domains