Multigrid techniques for finite elements on locally refined meshes

A robust and stable hybrid neural network/finite element method for 2D flows that generalizes to different geometries

“…n < 1×10 -8 or after a maximum of 10 iterations. The linear systems in each Newton step are solved with the GMRES method [53] preconditioned with a V-cycle geometric multigrid [54]. Internally, a shared-memory parallel Vanka smoother is used, see [55] for more details on the efficient implementation.…”

A robust and stable hybrid neural network/finite element method for 2D flows that generalizes to different geometries

“…n < 1×10 -8 or after a maximum of 10 iterations. The linear systems in each Newton step are solved with the GMRES method [53] preconditioned with a V-cycle geometric multigrid [54]. Internally, a shared-memory parallel Vanka smoother is used, see [55] for more details on the efficient implementation.…”

The deal.II library, Version 9.3

“…In contrast, the current release now also supports "global coarsening" algorithms [14,60] when using continuous (FE_Q, FE_SimplexP) and discontinuous (FE_DGQ, FE_SimplexDGP) elements. Global coarsening builds multigrid levels for the entire domain, coarsening all cells of a triangulation regardless of how many times they have been refined.…”

A next-generation discontinuous galerkin fluid dynamics solver with application to high-resolution lung airflow simulations

“…For this work, we have extended the above-described algorithm to deal with locally refined meshes in a forest-of-octrees description. Specifically, new algorithms for the construction of geometric levels via a procedure known as global coarsening [9,56] have been added to the deal.II finite element library [4]: towards the next coarser level, each cell is coarsened if possible; the coarse grid is obtained once none of the remaining cells can be coarsened further. While this approach potentially involves more work on each level than local-smoothing algorithms [14], global-coarsening algorithms promise simpler load-balancing with better parallel efficiency and fewer iterations.…”

A robust and stable hybrid neural network/finite element method for 2D flows that generalizes to different geometries

“…n < 1×10 -8 or after a maximum of 10 iterations. The linear systems in each Newton step are solved with the GMRES method [53] preconditioned with a V-cycle geometric multigrid [54]. Internally, a shared-memory parallel Vanka smoother is used, see [55] for more details on the efficient implementation.…”

The deal.II library, Version 9.3

“…In contrast, the current release now also supports "global coarsening" algorithms [14,60] when using continuous (FE_Q, FE_SimplexP) and discontinuous (FE_DGQ, FE_SimplexDGP) elements. Global coarsening builds multigrid levels for the entire domain, coarsening all cells of a triangulation regardless of how many times they have been refined.…”

A next-generation discontinuous galerkin fluid dynamics solver with application to high-resolution lung airflow simulations

“…For this work, we have extended the above-described algorithm to deal with locally refined meshes in a forest-of-octrees description. Specifically, new algorithms for the construction of geometric levels via a procedure known as global coarsening [9,56] have been added to the deal.II finite element library [4]: towards the next coarser level, each cell is coarsened if possible; the coarse grid is obtained once none of the remaining cells can be coarsened further. While this approach potentially involves more work on each level than local-smoothing algorithms [14], global-coarsening algorithms promise simpler load-balancing with better parallel efficiency and fewer iterations.…”

A robust and stable hybrid neural network/finite element method for 2D flows that generalizes to different geometries

“…n < 1×10 -8 or after a maximum of 10 iterations. The linear systems in each Newton step are solved with the GMRES method [53] preconditioned with a V-cycle geometric multigrid [54]. Internally, a shared-memory parallel Vanka smoother is used, see [55] for more details on the efficient implementation.…”

The deal.II library, Version 9.3

“…In contrast, the current release now also supports "global coarsening" algorithms [14,60] when using continuous (FE_Q, FE_SimplexP) and discontinuous (FE_DGQ, FE_SimplexDGP) elements. Global coarsening builds multigrid levels for the entire domain, coarsening all cells of a triangulation regardless of how many times they have been refined.…”

A next-generation discontinuous galerkin fluid dynamics solver with application to high-resolution lung airflow simulations

“…For this work, we have extended the above-described algorithm to deal with locally refined meshes in a forest-of-octrees description. Specifically, new algorithms for the construction of geometric levels via a procedure known as global coarsening [9,56] have been added to the deal.II finite element library [4]: towards the next coarser level, each cell is coarsened if possible; the coarse grid is obtained once none of the remaining cells can be coarsened further. While this approach potentially involves more work on each level than local-smoothing algorithms [14], global-coarsening algorithms promise simpler load-balancing with better parallel efficiency and fewer iterations.…”