Real-time finite element method for interactive design

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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.