Séance Séminaire

Séminaire ACSIOM

An optimization-based method for the numerical approximation of sign-changing PDEs

We are interested in physical settings presenting an interface between a classical (positive) material and a (negative) metamaterial, in such a way that the coefficients of the model change sign in the domain. We study, in the "elliptic" case, the numerical approximation of such sign-shifting problems. We introduce a new numerical method, based on domain decomposition and optimization, that we prove to be convergent, as soon as, for a given right-hand side, the problem admits a solution that is unique. The proof of convergence does not rely on any symmetry assumption on the mesh family with respect to the sign-changing interface. In that respect, it gives a more convenient alternative to T-coercivity based approximation in the situations when the latter is applicable, whereas it constitutes a new paradigm in the situations when the latter is not. We illustrate our findings on a comprehensive set of test-cases.