Refinement of polygonal grids using Convolutional Neural Networks with applications to polygonal Discontinuous Galerkin and Virtual Element methods
arXiv:2102.05738 · doi:10.1016/j.jcp.2021.110900
Abstract
We propose new strategies to handle polygonal grids refinement based on Convolutional Neural Networks (CNNs). We show that CNNs can be successfully employed to identify correctly the "shape" of a polygonal element so as to design suitable refinement criteria to be possibly employed within adaptive refinement strategies. We propose two refinement strategies that exploit the use of CNNs to classify elements' shape, at a low computational cost. We test the proposed idea considering two families of finite element methods that support arbitrarily shaped polygonal elements, namely Polygonal Discontinuous Galerkin (PolyDG) methods and Virtual Element Methods (VEMs). We demonstrate that the proposed algorithms can greatly improve the performance of the discretization schemes both in terms of accuracy and quality of the underlying grids. Moreover, since the training phase is performed off-line and is independent of the differential model the overall computational costs are kept low.
References in corpus (2)
Cited by in corpus (7)
- Machine Learning based refinement strategies for polyhedral grids with applications to Virtual Element and polyhedral Discontinuous Galerkin methods
- A Deep Learning algorithm to accelerate Algebraic Multigrid methods in Finite Element solvers of 3D elliptic PDEs
- Accelerating Algebraic Multigrid Methods via Artificial Neural Networks
- High order well-balanced Arbitrary-Lagrangian-Eulerian ADER discontinuous Galerkin schemes on general polygonal moving meshes
- Mesh Optimization for the Virtual Element Method: How Small Can an Agglomerated Mesh Become?
- R3MG: R-tree based agglomeration of polytopal grids with applications to multilevel methods
- Adaptive VEM: Stabilization-Free A Posteriori Error Analysis and Contraction Property