使用局部减少基底方法,对修剪的多贴片同地几何基尔霍夫 - 爱贝进行快速参数分析
Margarita Chasapi1, Pablo Antolin1, Annalisa Buffa1,2
1Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.
概括
本研究引入了一个新的模型订单减少框架,用于高效的Kirchhoff-Love贝实时模拟. 该方法显著降低了参数形状优化问题的计算成本.
科学领域:
- 计算力学是计算力学.
- 数字分析 数字分析
- 几何建模的几何建模.
背景情况:
- 为设计和形状优化执行多个模拟是计算密集的.
- 具有剪切,多补丁域的同位几何基尔霍夫 - 爱贝由于取决于几何的,非亲属运算符而带来了挑战.
- 参数变化可以在修剪的域中导致高度分歧的解决方案.
研究的目的:
- 开发一个高效的模型订单减少 (MOR) 框架,用于实时解决修剪的多补丁异地几何基尔霍夫 - 爱贝的解决方案.
- 为了解决参数研究和形状优化中的众多模拟的计算费用.
- 为了能够在不同的参数下准确和快速分析复杂的几何形状.
主要方法:
- 采用局部减少基础方法与集群技术相结合.
- 使用离散实证插位方法 (DEIM) 进行亲属近似.
- 将减少策略应用于参数形状优化问题.
- 在复杂几何形状的剪裁,多贴片网格上测试框架.
主要成果:
- 拟议的框架实现在线计算成本的显著降低,与标准的减少基础方法相比.
- 这种方法在解决参数化的Kirchhoff-Love shells方面表现出准确性.
- 实现了对几何依赖运算符和非亲系参数依赖性的高效处理.
结论:
- 开发的MOR框架提供了一个准确且计算效率高的解决方案,用于实时分析修剪的,多补丁的同位几何基尔霍夫-爱贝.
- 这种方法特别有利于参数形状优化,使设计代速度更快.
- 该框架有效地管理复杂的几何和参数变化,优于传统方法.
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