Closed Form Inverse of Local Multi-Trace Operators

摘要

We have shown in this paper that it is possible for the local multi-trace operator of a model transmission problem to obtain a closed form for the inverse. This would therefore be an ideal preconditioner for local multi-trace formulations. We are currently investigating if such closed form inverses are also possible for more general situations, where the coefficients are only constant in each subdomain, and in the presence of more subdomains. The closed form inverse seems to be inherent to the formulation, and not dependent on the specific form of the partial differential equation.