This contribution presents a model order reduction framework for real-time efficient solution of trimmed, multi-patch isogeometric Kirchhoff-Love shells. In several scenarios, such as design and shape optimization, multiple simulations need to be performed for a given set of physical or geometrical parameters. This step can be computationally expensive in particular for real world, practical applications. We are interested in geometrical parameters and take advantage of the flexibility of splines in representing complex geometries. In this case, the operators are geometry-dependent and generally depend on the parameters in a non-affine way. Moreover, the solutions obtained from trimmed domains may vary highly with respect to different values of the parameters. Therefore, we employ a local reduced basis method based on clustering techniques and the Discrete Empirical Interpolation Method to construct affine approximations and efficient reduced order models. In addition, we discuss the application of the reduction strategy to parametric shape optimization. Finally, we demonstrate the performance of the proposed framework to parameterized Kirchhoff-Love shells through benchmark tests on trimmed, multi-patch meshes including a complex geometry. The proposed approach is accurate and achieves a significant reduction of the online computational cost in comparison to the standard reduced basis method.

翻译：本文提出了一种模型降阶框架，用于实时高效求解裁剪多片等几何Kirchhoff-Love壳问题。在诸如设计与形状优化等场景中，需针对给定物理或几何参数集执行多次仿真。对于实际工程应用而言，这一步骤的计算成本可能极为高昂。本文聚焦于几何参数，并利用样条函数在复杂几何表征中的灵活性。在此情形下，算子具有几何依赖性，且通常以非仿射方式依赖于参数。此外，裁剪域求解结果可能随参数值的不同而产生显著变化。因此，我们采用基于聚类技术与离散经验插值法的局部简化基方法，构建仿射近似与高效降阶模型。同时，本文讨论了降阶策略在参数化形状优化中的应用。最后，通过包含复杂几何结构的裁剪多片网格基准测试，验证了所提框架在参数化Kirchhoff-Love壳问题中的性能。研究表明，该方法具有较高精度，且相比标准简化基方法，在线计算成本显著降低。