Projection based model order reduction has become a mature technique for simulation of large classes of parameterized systems. However, several challenges remain for problems where the solution manifold of the parameterized system cannot be well approximated by linear subspaces. While the online efficiency of these model reduction methods is very convincing for problems with a rapid decay of the Kolmogorov n-width, there are still major drawbacks and limitations. Most importantly, the construction of the reduced system in the offline phase is extremely CPU-time and memory consuming for large scale and multi scale systems. For practical applications, it is thus necessary to derive model reduction techniques that do not rely on a classical offline/online splitting but allow for more flexibility in the usage of computational resources. A promising approach with this respect is model reduction with adaptive enrichment. In this contribution we investigate Petrov-Galerkin based model reduction with adaptive basis enrichment within a Trust Region approach for the solution of multi scale and large scale PDE constrained parameter optimization.
翻译:以预测为基础的示范订单削减已成为模拟大型参数化系统类别的成熟技术,然而,在参数化系统的多种解决办法无法用线性子空间加以十分接近的问题方面,仍然存在若干挑战。虽然这些模型削减方法的在线效率对于科尔莫戈罗夫 n-width迅速衰减的问题非常令人信服,但仍存在重大缺陷和限制。最重要的是,在离线阶段建造减少的系统在大型和多级系统方面消耗了极多的CPU-时间和记忆。因此,在实际应用方面,有必要得出不依赖传统的离线/在线分离但允许在计算资源使用方面有更大灵活性的模型削减技术。在这方面,一个很有希望的方法是减少适应性浓缩的模型。在这个贡献中,我们调查了基于Petrov-Galerkin模型的削减,在“信托区域”办法内进行适应性基础浓缩,以解决多级和大规模PDE受限制的参数优化。