Preconditioning the augmented Lagrangian method for instationary mean field games with diffusion
Résumé
We apply the augmented Lagrangian method to the convex optimization problem of the instationary variational mean field games with diffusion. The system is first discretized with space-time tensor product piecewise polynomial bases. This leads to a sequence of linear problems posed on the space-time cylinder that are second order in the temporal variable and fourth order in the spatial variable. To solve these large linear problems with the preconditioned conjugate gradients method we propose a parameter-robust preconditioner that is based on a temporal transformation coupled with a spatial multigrid. Numerical examples illustrate the method.
Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...