Closed Form Inverse of Local Multi-Trace Operators

Alan Ayala (1) , Xavier Claeys (1) , Victorita Dolean (2) , Martin J Gander (3)

1 ALPINES - Algorithms and parallel tools for integrated numerical simulations
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 Section de mathématiques [Genève]

Local Multi-Trace Formulations (local MTF) are block-sparse boundary integral equations adapted to elliptic PDEs with piece-wise constant coefficients (typically multi-subdomain scattering problems) only recently introduced in [Hiptmair & Jerez-Hanckes, 2012]. In these formulations, transmission conditions are enforced by means of local operators, so that only adjacent subdomains communicate. We are interested here in the inverse of local multi-trace operators. We show that this inverse can be obtained in closed form for a model problem with three subdomains in the special case where the coefficients are homogeneous. We illustrate our findings with a numerical experiment that shows that discretizing the closed form inverse gives indeed and approximate inverse of the discretized local multi-trace operator.

Domaines: Analyse numérique [math.NA]

Alan Ayala, Xavier Claeys, Victorita Dolean, Martin J Gander. Closed Form Inverse of Local Multi-Trace Operators. Domain Decomposition Methods in Science and Engineering XXIII, Jul 2015, Jeju island, South Korea. ⟨10.1007/978-3-319-52389-7_9⟩. ⟨hal-01427610⟩