Combining an a Priori Space-Time Separated Model-Order Reduction Technique to the Particle Finite Element Method
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The Particle Finite Element method is a fluid solver based on Lagrangian finite elements combined with efficient re-meshing algorithms [1]. It was shown to be effective in a large amount of applications, especially in the case of free surface fluids flows or fluid-structure interactions as the different interfaces are intrinsically dealt with within the method. Up to now, this method has never been paired up with any model-order reduction technique because of the difficulties linked to the re-meshing schemes. This remains however, an important area of research to uncover as it could drastically reduce the computational cost of the method. In this work, we focus on an a priori reduction method called Proper Generalized Decomposition (PGD) with a space-time decomposition.
