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.

We derive an effective transmission condition for acoustic subwavelength resonators, modeled as small-scaled bubbles distributed not necessarily periodically along a smooth, bounded hypersurface, which need not be flat. The transmission condition relates the jump in the normal derivative of the acoustic field to its second time derivative, convoluted in time with a sinusoidal kernel. This kernel has a period determined by the common subwavelength resonance (specifically, the Minnaert resonance in this case). This dispersive transmission condition can also be interpreted as a Dirac-like surface potential that is convoluted in the time domain and spatially supported on the specified hypersurface, unveils distinct regimes of acoustic behavior: 1. Low resonance: The surface becomes fully transparent, allowing complete acoustic transmission; 2. Moderate resonance: The surface exhibits memory effects, acting as a dispersive acoustic screen; 3. High resonance: The surface functions as a partially reflective or transmissive state with negligible memory effect. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.