5 research outputs found
A Note on Ribbon-based Biharmonic Surface Patches
In this short note we describe a simple adaptation of biharmonic surfaces to
interpolate boundary cross-derivatives given in ribbon form, and compare with
the recently proposed Generalized B-spline patches
PDE-Based Parameterisation Techniques for Planar Multipatch Domains
This paper presents a PDE-based parameterisation framework for addressing the
planar surface-to-volume (StV) problem of finding a valid description of the
domain's interior given no more than a spline-based description of its boundary
contours. 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 and
propose several PDE-based problem formulations capable of finding a valid map
between a convex parametric multipatch domain and the piecewise-smooth physical
domain with an equal number of sides. In line with the isoparametric paradigm
of IGA, we treat the StV problem using techniques that are characteristic for
the analysis step. As such, this study proposes several IGA-based numerical
algorithms for the problem's governing equations that can be effortlessly
integrated into a well-developed IGA software suite. We augment the framework
with mechanisms that enable controlling the parametric properties of the
outcome. Parametric control is accomplished by, among other techniques, the
introduction of a curvilinear coordinate system in the convex parametric domain
that, depending on the application, builds desired features into the computed
harmonic map, such as homogeneous cell sizes or boundary layers