A Deep Learning algorithm to accelerate Algebraic Multigrid methods in Finite Element solvers of 3D elliptic PDEs

Understand

Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs).

• The most severe limitation of AMG methods is the dependence on parameters that require to be fine-tuned.
• In particular, the strong threshold parameter is the most relevant since it stands at the basis of the construction of successively coarser grids needed by the AMG methods.
• We introduce a novel Deep Learning algorithm that minimizes the computational cost of the AMG method when used as a finite element solver.