We propose two new strategies based on Machine Learning techniques to handle polyhedral grid refinement, to be possibly employed within an adaptive framework. The first one employs the k-means clustering algorithm to partition the points of the polyhedron to be refined. This strategy is a variation of the well known Centroidal Voronoi Tessellation. The second one employs Convolutional Neural Networks to classify the “shape” of an element so that “ad-hoc” refinement criteria can be defined. This strategy can be used to enhance existing refinement strategies, including the k-means strategy, at a low online computational cost. We test the proposed algorithms considering two families of finite element methods that support arbitrarily shaped polyhedral elements, namely the Virtual Element Method (VEM) and the Polygonal Discontinuous Galerkin (PolyDG) method. We demonstrate that these strategies do preserve the structure and the quality of the underlaying grids, reducing the overall computational cost and mesh complexity.

Antonietti, P., Dassi, F., Manuzzi, E. (2022). Machine learning based refinement strategies for polyhedral grids with applications to virtual element and polyhedral discontinuous Galerkin methods. JOURNAL OF COMPUTATIONAL PHYSICS, 469(15 November 2022) [10.1016/j.jcp.2022.111531].

Machine learning based refinement strategies for polyhedral grids with applications to virtual element and polyhedral discontinuous Galerkin methods

F. Dassi
;
2022

Abstract

We propose two new strategies based on Machine Learning techniques to handle polyhedral grid refinement, to be possibly employed within an adaptive framework. The first one employs the k-means clustering algorithm to partition the points of the polyhedron to be refined. This strategy is a variation of the well known Centroidal Voronoi Tessellation. The second one employs Convolutional Neural Networks to classify the “shape” of an element so that “ad-hoc” refinement criteria can be defined. This strategy can be used to enhance existing refinement strategies, including the k-means strategy, at a low online computational cost. We test the proposed algorithms considering two families of finite element methods that support arbitrarily shaped polyhedral elements, namely the Virtual Element Method (VEM) and the Polygonal Discontinuous Galerkin (PolyDG) method. We demonstrate that these strategies do preserve the structure and the quality of the underlaying grids, reducing the overall computational cost and mesh complexity.
Articolo in rivista - Articolo scientifico
Convolutional neural networks; k-means; Machine learning; Polyhedral discontinuous Galerkin; Polyhedral grid refinement; Virtual element method;
English
12-ago-2022
2022
469
15 November 2022
111531
none
Antonietti, P., Dassi, F., Manuzzi, E. (2022). Machine learning based refinement strategies for polyhedral grids with applications to virtual element and polyhedral discontinuous Galerkin methods. JOURNAL OF COMPUTATIONAL PHYSICS, 469(15 November 2022) [10.1016/j.jcp.2022.111531].
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/394875
Citazioni
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 6
Social impact