Multipatch Coupling via a Gap-Based Shifted Boundary Method: Applications to Isogeometric Analysis

  • Zorrilla, Rubén (UPC & CIMNE)
  • Antonelli, Nicolò (CIMNE)
  • Gorgi, Andrea (CIMNE)
  • Rossi, Riccardo (UPC & CIMNE)
  • Scovazzi, Guglielmo (Duke University)

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This work presents a gap-based multipatch formulation of the Shifted Boundary Method (SBM) within the context of isogeometric analysis (IGA). The proposed approach addresses the coupling of independently discretized patches characterized by different parameterizations, polynomial orders, and mesh resolutions, without requiring mesh conformity or explicit interface reconstruction. The formulation leverages the SBM philosophy to treat patch interfaces through surrogate boundaries, enabling a consistent weak enforcement of continuity across nonmatching interfaces. Geometric gaps arising from trimming operations, CAD inconsistencies, or heterogeneous patch configurations are handled in a stable and systematic manner. The method preserves high-order accuracy and avoids the need for mortar spaces, Lagrange multipliers, or penalty-based tuning parameters typically required in multipatch coupling strategies. A key feature of the proposed approach is its robustness under strong discretization heterogeneity, including variations in spline degree and refinement levels across patches. The resulting scheme remains fully compatible with standard finite element infrastructures and retains the modular structure of multipatch IGA formulations. Numerical examples demonstrate optimal convergence rates, stability, and accurate interface transmission in representative multipatch configurations. The proposed gap-SBM formulation provides a flexible and scalable alternative for multipatch IGA coupling and opens the door to further extensions, including applications to sliding mesh coupling techniques.