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Multitrace formulations (MTFs) are based on a decomposition of the problemdomain into subdomains, and thus domain decomposition solvers are of interest.The fully rigorous mathematical MTF can however be daunting for thenon-specialist. We introduce in this paper MTFs on a simple model problem usingconcepts familiar to researchers in domain decomposition. This allows us to geta new understanding of MTFs and a natural block Jacobi iteration, for which wedetermine optimal relaxation parameters. We then show how iterative multitraceformulation solvers are related to a well known domain decomposition methodcalled optimal Schwarz method: a method which used Dirichlet to Neumann maps inthe transmission condition. We finally show that the insight gained from thesimple model problem leads to remarkable identities for Calderon projectors andrelated operators, and the convergence results and optimal choice of therelaxation parameter we obtained is independent of the geometry, the spacedimension of the problem{\color{black}, and the precise form of the spatialelliptic operator, like for optimal Schwarz methods. We illustrate our analysiswith numerical experiments.

An introduction to Multitrace Formulations and Associated Domain Decomposition Solvers