The Shifted Boundary Method in Isogeometric Analysis
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 mea...
| Autores: | , , , , , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2024 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/413651 |
| Acesso em linha: | https://hdl.handle.net/2117/413651 https://dx.doi.org/10.1016/j.cma.2024.117228 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Mathematical models Shifted Boundary Method (SBM) Isogeometric Analysis (IGA) Isogeometric Boundary Representation Analysis (IBRA) Unfitted boundary methods Small cut-cell problem Geometria computacional Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Modelització matemàtica |
| Resumo: | 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. |
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