A parallel coupling strategy for the Chimera and domain decomposition methods in computational mechanics

Domain Decomposition Methods (DDMs) are techniques that divide the solution of a PDE on a domain into smaller solutions on smaller subdomains coupling them using a certain strategy. They are used for essentially two purposes: designing parallel solvers and/or coupling subdomains with different meshes, different numerical approximations, etc. In this paper we are interested in this last category. One example of application is the Chimera method. In that sense, the Chimera method can be viewed as a preprocess technique plus a DDM on overlapping and non-conforming subdomains. The coupling technique of DDM is usually achieved via transmission conditions to impose the continuities of the unknown and its flux across the subdomain boundaries. We propose in this work an alternative coupling strategy, intervening as a preprocess method. It consists in connecting the nodes of one subdomain with the nodes of the adjacent subdomains via newly created elements. In this way, the multi-domain character of a DDM disappears, making it a parallel, implicit and versatile method. We discuss in this paper the relation between the proposed method and the existing coupling strategies. We also present some convergence results as well as some applications to the Navier–Stokes equations and other PDE’s.