Convolution Hierarchical Deep-Learning Neural Network Tensor Decomposition (C-HiDeNN-TD) for high-resolution topology optimization

This paper explores numerical methods dedicated to 3D elastic waves simulations in spatially separable domains such as plates. The objective is to reduce the computation time and the memory requirements associated to these large simulations involving fine space and time discretizations. The 3D problem is decomposed into a sequence of lower dimensional problems with the Proper Generalized Decomposition. The spatial discretization is performed with the Spectral Element Method to provide more compact separated representations compared to the ones obtained with a finite element discretization. Following previous works on space separation in elastodynamics, we explore hybrid explicit/implicit time marching schemes to improve the solution through one direction as needed, without decreasing the time step due to stability constraints. Large 3D numerical problems with several millions of degrees of freedom are efficiently solved with memory requirements characteristic of 2D problems. 

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Exploring space separation techniques for 3D elastic waves simulations

Development of POD-based Reduced Order Models applied to shallow water equations using augmented Riemann solvers

Proper Generalized Decomposition using Taylor expansion for non-linear diffusion equations

Development of Pod-Based Reduced Order Models Applied to Shallow Water Equations Using Augmented Riemann Solvers

https://hal.archives-ouvertes.fr/hal-03192076/document

Dimitri Goutaudier

Papers

Proper Generalized Decomposition with time adaptive space separation for transient wave propagation problems in separable domains