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.

中文翻译：

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等几何分析中的移动边界法


这项工作提出了等几何分析 (IGA) 框架内移动边界法 (SBM) 的新颖应用，将其应用于具有狄利克雷和诺依曼边界条件的二维和三维泊松问题。 SBM 边界条件施加是通过完全无惩罚公式实现的，无需惩罚校准。数值实验证明了阶数提升与通过高阶泰勒展开式的 SBM 相结合如何始终实现最佳收敛速度。此外，分析问题矩阵的条件数表明，当 SBM 与 IGA 集成时，可以有效地避免小切割单元问题，这是边界不拟合的数值方法中的常见问题。