Recursive formulation and parallel implementation of multiscale mixed methods

Multiscale methods for second order elliptic equations based on non-overlapping domain decomposition schemes have great potential to take advantage of multi-core, state-of-the-art parallel computers. These typically involve solving local boundary value problems followed by the solution a global interface problem. Known iterative procedures problem slow convergence, increasing overall cost multiscale solver. To overcome this we develop scalable recursive method such that replaces family small systems associated with adjacent subdomains, in hierarchy nested subdomains. Then, propose novel algorithm implement our formulation multi-core devices using Robin Coupled Method Guiraldello et al. (2018) [26], can be seen as generalization several mixed methods. Through numerical studies show new is very fast and exhibits excellent strong weak scalability. We consider large problems, billions discretization cells, motivated simulation subsurface flows.