Compatible Coarse Nodal and Edge Elements Through Energy Functionals

François Musy (1) , Laurent Nicolas (2) , Ronan Perrussel (1, 2)

1 ICJ - Institut Camille Jordan
2 AMPERE - Ampère

We propose new algorithms for the setup phase of algebraic multigrid AMG) solvers for linear systems coming from edge element discretization. The construction of coarse levels is performed by solving an optimization problem with a Lagrange multiplier method: we minimize the energy of coarse bases under a constraint linking coarse nodal and edge element bases. On structured meshes, the resulting AMG method and the geometric multigrid method behave similarly as preconditioners. On unstructured meshes, the convergence rate of our method compares favorably with the AMG method of Reitzinger and Schöberl.

Mots clés: multigrid; constrained optimization; edge finite elements

Domaines: Analyse numérique [cs.NA]; Electromagnétisme

François Musy, Laurent Nicolas, Ronan Perrussel. Compatible Coarse Nodal and Edge Elements Through Energy Functionals. SIAM Journal on Scientific Computing, 2007, 29 (3), pp.1315--1337. ⟨10.1137/050645750⟩. ⟨hal-00153809⟩