Real-time finite element method for interactive design

典型的工程设计过程是迭代的，涉及到评估一组“如果？”场景。对于任何零部件或组件，这可能涉及对几何图形进行微小更改、选择不同的材料、评估不同类型的紧固件或测试设计对一系列边界条件的响应。此外，在安全关键应用中，设计过程可能会着眼于新制造的部件并预测安全工作寿命，同时考虑到随着时间的推移缺陷积累的影响。可以使用单一的有限元分析来评估每个单独的方案。使用标准工具，每个分析的有限元求解过程通常从一组新的方程重新开始。如果能设计一种新的数值方法来重复使用以前的每一次分析的结果，以加快每一次后续分析的求解速度，我们应该能够加速这一过程，以便我们能够交互地实时修改和评估设计。这个概念被称为重新分析，只有几个研究人员对这个主题进行了研究。在这个项目中，起点将是调查一组常见的求解技术--Krylov子空间解算器--是否可以适用于使用机器学习技术进行重新分析。该项目将评估新的交互式再分析工具，以设计聚变反应堆的面向等离子体的壁和/或类似复杂的聚变反应堆设计挑战。

The typical engineering design process is iterative and involves evaluating a set of "What if?" scenarios. For any component or assembly, this may involve making small changes to the geometry, selecting different materials, evaluating different types of fastenings or testing the response of the design to a range of boundary conditions. Furthermore, in safety critical applications, the design process may look beyond the newly manufactured component and predict safe working life, taking into account the effect of the accumulation of defects over time. Each individual scenario may be evaluated using a single finite element analysis. Using standard tools, the finite element solution process for each analysis usually restarts with a new set of equations. If one could design a novel numerical method to reuse the results of each previous analysis to speed up the solution of each subsequent analysis, we should be able to accelerate the process so that we can interactively modify and evaluate the design in real-time. This concept is called reanalysis and only a few researchers have looked into the topic. In this project, the starting point will be to investigate whether a common set of solution techniques, Krylov subspace solvers, can be adapted for reanalysis using machine learning techniques. The project will evaluate the new interactive reanalysis tool for the design of the plasma facing wall of a fusion reactor and/or similarly complex fusion reactor design challenges.