The Shifted Boundary Method in Isogeometric Analysis
2024
Antonelli, Nicolò | Aristio, Ricky | Gorgi, Andrea | Zorrilla Martínez, Rubén | Rossi, Riccardo | Scovazzi, Guglielmo | Wüchner, Roland | Universitat Politècnica de Catalunya. Doctorat en Anàlisi Estructural | Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental | Centre Internacional de Mètodes Numèrics en Enginyeria
This work presents a novel application of the Shifted Boundary Method (SBM) within the Isogeometric Analysis (IGA) framework, applying it to two-dimensional and three-dimensional Poisson problems with Dirichlet and Neumann boundary conditions. The SBM boundary condition imposition is achieved by means of a fully penalty-free formulation, eliminating the need for penalty calibration. The numerical experiments demonstrate how order elevation, coupled with SBM through higher-order Taylor expansions, consistently achieves optimal convergence rates. Additionally, analyzing the condition number of the problem matrix reveals that SBM, when integrated with IGA, effectively circumvents the small cut-cell problem, a common issue in numerical methods with unfitted boundaries.
显示更多 [+] 显示较少 [-]Peer Reviewed
显示更多 [+] 显示较少 [-]Postprint (published version)
显示更多 [+] 显示较少 [-]