Enabling Multidisciplinary Design Optimization: Inexact-Newton-Krylov and the Individual-Discipline-Feasible Formulation

该项目正在研究无矩阵牛顿-克里洛夫算法，以此作为解决多学科设计优化问题的一种手段。更准确地说，我们正在探索使用无矩阵算法来以模块化方式解决基于模拟的设计优化问题。模块化对于这些问题很有吸引力，因为许多遗留软件库已经存在，可以分析和优化涉及单个学科的问题，例如流体动力学。相比之下，很少有图书馆可以分析复杂的多学科系统，更不用说优化它们了。为了实现模块化办法，我们采用了所谓的个人纪律可行(IDF)提法。在历史上，IDF公式一直受到传统优化算法所要求的形成计算量大的矩阵的需要的限制。这激发了我们对牛顿-克里洛夫算法的研究，它将使IDF的可扩展和无矩阵实现成为可能。由复杂的多物理管理的工程系统在设计上具有挑战性，因为它们经常表现出微妙的权衡，并违背我们的直觉。当用高保真模拟精确地模拟物理时，数值优化可以帮助指导和指导复杂工程系统的设计。通过展示无矩阵的牛顿-克里洛夫方法可以有效地解决IDF公式的问题，该项目承诺使高保真设计优化更容易处理和更容易实施的工业从业者。这使得强大的优化工具对设计师更有用，导致改进的产品和工艺造福社会；例如，排放更低的飞机、更高效的发电厂和更好的人造心脏。这些工具还可以简化设计过程，这将提高国内行业的经济竞争力。

This project is investigating matrix-free Newton-Krylov algorithms as a means of solving multidisciplinary design optimization problems. More precisely, we are exploring the use of matrix-free algorithms to solve simulation-based design optimization problems in a modular way. Modularity is attractive for these problems because many legacy software libraries already exist that can analyze and optimize problems involving a single discipline, for example fluid dynamics. In contrast, few libraries are available that can analyze complex multidisciplinary systems, let alone optimize them. To achieve a modular approach, we have adopted the so-called individual-discipline-feasible (IDF) formulation. Historically, the IDF formulation has been limited by the need to form computationally expensive matrices demanded by conventional optimization algorithms. This motivates our investigation of Newton-Krylov algorithms, which will enable a scalable and matrix-free implementation of IDF.Engineering systems governed by complex multi-physics are challenging to design, because they often exhibit subtle tradeoffs and defy our intuition. When the physics are modeled accurately with high-fidelity simulations, numerical optimization can help guide and inform the design of complex engineering systems. By showing that matrix-free Newton-Krylov methods can be used to efficiently solve IDF-formulated problems, this project promises to make high-fidelity design optimization more tractable and easier to implement for industrial practitioners. This makes powerful optimization tools more useful to designers, leading to improved products and processes that benefit society; examples include aircraft with lower emissions, more efficient power plants, and better artificial hearts. Such tools can also streamline the design process, which would improve the economic competitiveness of domestic industries.