Closed form inverse of local multi-trace operators

Ayala, Alan and Claeys, Xavier and Dolean, Victorita and Gander, Martin J.; Lee, Chang-Ock and Cai, Xiao-Chuan and Keyes, David E. and Kim, Hyea Hyun and Klawonn, Axel and Park, Eun-Jae and Widlund, Olof B., eds. (2017) Closed form inverse of local multi-trace operators. In: Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering . Springer-Verlag, KOR, pp. 107-115. ISBN 9783319523880 (

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Local multi-trace formulations are a way to express transmission problems. They are based on integral formulations of the solution on each subdomain, and between the subdomains both the known jumps in the traces and the fluxes of the transmission problem are imposed, and thus the method contains multiple traces in its formulation. We show in this paper that it is possible to derive a closed form inverse for local multi-trace operators for an elliptic model problem.