MS-GIFT: Multi-Sided Geometry-Independent Field ApproximaTion Approach for Isogeometric Analysis

The Geometry-Independent Field approximaTion (GIFT) technique, an extension of isogeometric analysis (IGA), allows for separate spaces to parameterize the computational domain and approximate solution field. Based on the GIFT approach, this paper proposes a novel IGA methodology that incorporates toric surface patches for multi-sided geometry representation, while utilizing B-spline or truncated hierarchical B-spline (THB-spline) basis for analysis. By creating an appropriate bijection between the parametric domains of distinct bases for modeling and approximation, our method ensures smoothness within the computational domain and combines the compact support of B-splines or the local refinement potential of THB-splines, resulting in more efficient and precise solutions. To enhance the quality of parameterization and consequently boost the accuracy of downstream analysis, we suggest optimizing the composite toric parameterization. Numerical examples validate the effectiveness and superiority of our suggested approach.