An introduction to Multitrace Formulations and Associated Domain Decomposition Solvers
Résumé
Multitrace formulations (MTFs) are based on a decomposition of the problem domain
into subdomains, and thus domain decomposition solvers are of interest. The fully rigorous
mathematical MTF can however be daunting for the non-specialist. We introduce in this paper
MTFs on a simple model problem using concepts familiar to researchers in domain decomposition.
This allows us to get a new understanding of MTFs and a natural block Jacobi iteration, for which
we determine optimal relaxation parameters. We then show how iterative multitrace formulation
solvers are related to a well known domain decomposition method called optimal Schwarz method:
a method which used Dirichlet to Neumann maps in the transmission condition. We nally show
that the insight gained from the simple model problem leads to remarkable identities for Calderon
projectors and related operators, and the convergence results and optimal choice of the relaxation
parameter we obtained is independent of the geometry, the space dimension of the problem, and
the precise form of the spatial elliptic operator, like for optimal Schwarz methods. We illustrate our
analysis with numerical experiments.
Domaines
Analyse numérique [math.NA]Origine | Fichiers produits par l'(les) auteur(s) |
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