Dual-primal Isogeometric Tearing and Interconnecting Solvers for adaptively refined multi-patch configurations

Abstract: Isogeometric Analysis is a variant of the finite element method, where spline functions are used for the representation of both the geometry and the solution. Splines, particularly those with higher degree, achieve their full approximation power only if the solution is sufficiently regular. Since solutions are usually not regular everywhere, adaptive refinement is essential. Recently, a multi-patch-based adaptive refinement strategy based on recursive patch splitting has been proposed, which naturally generates hierarchical, non-matching multi-patch configurations with T-junctions, but preserves the tensor-product structure within each patch. In this work, we investigate the application of the dual-primal Isogeometric Tearing and Interconnecting method (IETI-DP) to such adaptive multi-patch geometries. We provide sufficient conditions for the solvability of the local problems and propose a preconditioner for the overall iterative solver. We establish a condition number bound that coincides with the bound previously shown for the fully matching case. Numerical experiments confirm the theoretical findings and demonstrate the efficiency of the proposed approach in adaptive refinement scenarios.