  Isogeometric analysis has brought a paradigm shift in integrating
computational simulations with geometric designs across engineering
disciplines. This technique necessitates analysis-suitable parameterization of
physical domains to fully harness the synergy between Computer-Aided Design and
Computer-Aided Engineering analyses. The existing methods often fix boundary
parameters, leading to challenges in elongated geometries such as fluid
channels and tubular reactors. This paper presents an innovative solution for
the boundary parameter matching problem, specifically designed for
analysis-suitable parameterizations. We employ a sophisticated
Schwarz-Christoffel mapping technique, which is instrumental in computing
boundary correspondences. A refined boundary curve reparameterization process
complements this. Our dual-strategy approach maintains the geometric exactness
and continuity of input physical domains, overcoming limitations often
encountered with the existing reparameterization techniques. By employing our
proposed boundary parameter method, we show that even a simple linear
interpolation approach can effectively construct a satisfactory
analysis-suitable parameterization. Our methodology offers significant
improvements over traditional practices, enabling the generation of
analysis-suitable and geometrically precise models, which is crucial for
ensuring accurate simulation results. Numerical experiments show the capacity
of the proposed method to enhance the quality and reliability of isogeometric
analysis workflows.
