Automatic stabilization of finite-element simulations using neural networks and hierarchical matrices

no code implementations • 24 Dec 2022 • Tomasz Sluzalec, Mateusz Dobija, Anna Paszynska, Ignacio Muga, Maciej Paszynski

Petrov-Galerkin formulations with optimal test functions allow for the stabilization of finite element simulations.

Quasi-optimal $hp$-finite element refinements towards singularities via deep neural network prediction

no code implementations • 13 Sep 2022 • Tomasz Sluzalec, Rafal Grzeszczuk, Sergio Rojas, Witold Dzwinel, Maciej Paszynski

We aim to construct the DNN expert to identify quasi-optimal $hp$ refinements of the coarse mesh elements.