An efficient parametrization of planar domain for isogeometric analysis using harmonic functions

Abstract

A recent and unified methodology of isogeometric analysis (IGA) requires the geometric model of the domain in the form of a parametric spline. Developing such a geometric model for IGA is called parameterization, and it is a challenging task. The way quality of a mesh affects the results in finite element analysis; an effective parametrization is a key for accurate results and computational efficiency. Finding a spline representation for the domain involves two sets of unknowns, namely parameter values and control points. In this work, a new method is proposed to find them in two stages for planar domains. The domain is mapped to an equivalent convex domain using harmonic functions. Here, the domain is mapped to a circle and then to a square so that the resulting parameter values are suitable for the tensor–product form of B-spline surface. The B-spline control points for the domain are computed with inverse of tensor–product B-spline. Most existing methodologies involve iterative optimization-based methods which makes them expensive. Experimental results of a few cases of complex domains are reported to demonstrate the effectiveness of the method in comparison with other methods. Moreover, metrics are developed to assess the quality of parametrization are included.